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Turning a quarter to the left five times successively makes more than a cycle. That may be the correct explanation why the creator of the day calendar of Q quitted at noon.

But I suspect there is more to it than that. In old Egypt the left eye of the sun became the moon:

"According to Wilkinson very early sun and moon were understood as the eyes of the falcon god Horus. Later these eyes became differentiated and sun became the right eye (the eye of Ra), while moon became the left eye (the eye of Horus).

    

At left (from us seen) the eye of Ra, at right the eye of Horus (pictures from Wilkinson)."

Only the morning sun was thereafter the real sun, that is what I think, and I also think that we can find the two eyes in the sky depicted like this in the rongorongo texts:

"... The myth, therefore, I take it, simply means that the rising sun destroys the circumpolar stars. These stars are represented in the earliest forms of the myth either by the crocodile or the hippopotamus; of course they disappeared (or were killed) at sunrise.

Horus, the bright ray on the horizon, is victorious by destroying the crocodile and the hippopotamus, which represent the powers of darkness." (Lockyer)

The important sun is the one who lifts the darkness from earth, the morning sun. Marduk he was called in old Babylonia:

"Marduk, die Frühsonne des Tages und des Jahres, wurde eben wegen dieses seines Charakters der Lichtbringer am Weltmorgen.

Marduk, der die leblose, chaotische Nacht, die keine Gestaltungen erkennen lässt, besiegt, der den Winter mit seinem Wasserfluten, den Feind des Naturlebens, überwindet, wurde der Schöpfer des Lebens und der Bewegung, der Ordner des Regellosen, der Gestalter des Unförmlichen am Weltmorgen."

"Die Sonne, die des Morgens das Weltmeer durchschreitet und besiegt und das Licht bringt, lässt aus dem Chaos der Nacht zuerst den Himmel, dann erst die Erde hervortreten, spaltet das gestaltlose Reich der Nacht in die zwei Hälften, den Himmel und die Erde." (Jensen)

If we locate Marduk/Ra to a.m., then the center of their 'kingdom' will be at dawn. The Rapanui equivalent power at dawn surely is Tama the strong last-born son of Hotu Matu'a:

"The fourth child entered. Matua kissed him on both cheeks and asked, 'Who are you?' He answered, 'It is I, the last-born (hangu potu), Te Mata O Tuu Hotu Iti.' The king was glad and said, 'You are a very strong child (poki hiohio), oh last-born, I wish you luck! Swift (?) is the great shark of Motu Toremo Hiva, of the homeland!' That was the end of King Hotu A Matua's speech to his children." (Barthel 2)

Interesting is the example tama tôa, shoot of sugarcane. If we think about the 'stations' of the night as 'tôa' (in Metoro's tôa tauuru), then we may guess the meaning of the small 'baby appendices' at bottom right in Ha5-47--48:

They could be 'sugarcane' shoots (tama) of the new day. Are sugarcane shoots very strong? Are the stems strong enough to lift up the roof of the sky? Or is there a wordplay hinting at to'a (warriors) forcing the sky up under the leadership of their chief, the morning sun?

The shoot attatched to the ragi appendix (in Ha5-47) is smaller than the shoot attatched to the nuku (?) appendix (in Ha5-48). The sky is illuminated first, the earth later - a little shoot is an earlier appearance than a big shoot.

This Tama - strong young son of Hotu Matu'a - probably may be called Tama Nui te Ra.

Hotu Matu'a may have been a real person, but he was a solar king anyhow, and the solar myths were drawn to him.

"... It was during this struggle [of Maui and his men] with the sun that his second name was learned by man. At the height of his agony the sun cried out: 'Why am I treated by you in this way? Do you know what it is you are doing. O you men? Why do you wish to kill Tama nui te ra?' This was his name, meaning Great Son of the Day, which was never known before." (Maori Myths)

The secret revealed may have been the name Ra, the Egyptian name.

The threat to kill him implies that the scene of action was noon. At midsummer solstice the sun moves slowly and therefore his speed at noon should also be slower.

Having identified the dawn with Tama Nui te Ra, we may easily guess what the name of dusk could be:

 "... 'Look over there', said Makea, pointing to the ice-cold mountains beneath the flaming clouds of sunset. 'What you see there is Hine nui, flashing where the sky meets the earth. Her body is like a woman's, but the pupils of her eyes are greenstone and her hair is kelp. Her mouth is that of a barracuda, and in the place where men enter her she has sharp teeth of obsidian and greenstone.' ..." (Maori Myths) 

I suggest the name of dusk to be Hine Nui te Po.

The Y-sign in

should be pronounced 'po'; remember that we interpreted Aa1-26:

as the sun at Poike (with ike = tapa-beater).

The melody in saying Tama Nui te Ra is the same as that in Hine Nui te Po. These presumably are two of the four cardinal points.

There is probably no good reason to search for an Egyptian last name alternative to Po (in the same way as Ra was applied as a last name for Tama Nui). But according to D'Alleva there is another name for the dark goddess:

"The back-to-back motif reappears in a Tongan suspension hook carved of ivory.

Wooden hooks, sometimes painted with images but not figurally carved, were used in households to suspend bags of food, safeguarding them from rodents.

Both the material and the figural decoration of this hook suggest that it had a ceremonial function.

'... in fact, [on Fiji] images of animals or humans could be reproduced on religious artefacts only ...'

Single female figures of similar form are thought to represent ancestors or possibly Hikule'o, goddess of the afterlife."

Searching for the meaning of the word Hikule'o I find the following items:

If we leave the dusk and the period between dusk and midnight, we should perhaps return to Poike and add that as a third cardinal point to our list:

The use of po in the expression po-á (morning) may be the reason why we find Y-signs at the start of the day, e.g. in (Qa5-40):

To wish somebody good luck with the words po nui feels strange, but perhaps the idea is to say: 'I wish you will survive the night!'

 

The fourth cardinal point would be the one at midnight, probably henua lying down, maybe a threshold:

'... It is indeed 'the king standing in a gateway' and Soothill (5), p. 62, makes the suggestion that it refers to the emperor's station on the threshold between one room of the Ming Thang [Bright Palace, 'the mystical temple-dwelling which the emperor was supposed to frequent, carrying out the rites appropriate to the seasons'] and another when an intercalary month intervened in the normal cycle of his perambulation.'

I guess we could call the cardinal midnight point (it must be female if it is horizontal) Papa Tua Nuku.

The flat horizontal plane surely is papa. And we find this flat surface straight down under our feet, at the 'back' (tu'a) of our place of living (nuku).

The story which Q possibly relates (in the day calendar) is ending when sun is standing at his peak (Poike).

"peak¹ pointed extremity; projecting part of the brim of a cap ... pointed top of a mountain ..." (English Etymology)

"peak² ...  fall, tumble ...  shrink ... " (English Etymology)

The word tu'amoúga means mountain summit. But 'summit' presumably means 'sun-middle' and moúga is used also for 'last': e.g. in vânaga moúga o te Ariki O Hotu Matu'a, the last words of King Hotu Matu'a.

The story begins with the generation of the sun/son and tell us how he evolved into a vigorous child or 'shoot' (tama) - or fruit (hua) - in the empty dry carcass of his father (who died at dusk - like the father in the Hawaiian story about Mokuora, the Living Island).

It is a very old story that has echoed up through the ages, e.g. in old Egypt:

"The basic myth of dynastic Egypt was that of the death and resurrection of Osiris, the good king, 'fair of face', who was born to the earth-god Geb and sky-goddess Nut. He was born together with his sister-wife, the goddess Isis, during the sacred interval of those five supplementary days that fell between one Egyptian calendric year of 360 days and the next. He and his sister were the first to plant wheat and barley, to gather fruit from trees, and to cultivate the vine, and before their time the races of the world had been savage cannibals. 

But Osiris's evil brother, Set, whose sister-wife was the goddess Nephtys, was mortally jealous both of his virtue and of his fame, and so, stealthily taking the measure of his good brother's body, he caused a beautifully decorated sarcophagus to be fashioned and on a certain occasion in the palace, when all were drinking and making merry, had it brought into the room and jestingly promised to give it to the one whom it should fit exactly. 

All tried, but, like the glass slipper of Cinderella, it fitted but one; and when Osiris, the last, laid himself within it, immediately a company of seventy-two conspirators with whom Set had contrived his plot dashed forward, nailed the lid upon the sarcophagus, soldered it with molten lead, and flung it into the Nile, down which it floated to the sea. 

Isis, overwhelmed with grief, sheared off her locks, donned mourning, and searched in vain, up and down the Nile; but the coffin had been carried by the tide to the coast of Phoenicia, where, at Byblos, it was cast ashore. 

A tamarisk immediately grew up around it, enclosing the precious object in its trunk, and the aroma of this tree then was so glorious that the local king, and queen, Melqart and Astarte - who were, of course, a divine king and queen themselves, the local representatives, in fact, of the common mythology of Damuzi and Inanna, Tammuz and Ishtar, Adonis and Aphrodite, Osiris and Isis - discovering and admiring its beauty, had the tree felled and fashioned into a pillar of their palace. 

The bereaved and sorrowing Isis, meanwhile, wandering over the world in her quest - like Demeter in search of the lost Persephone - came to Byblos, where she learned of the wonderful tree. And, placing herself by a well of the city, in mourning, veiled and in humble guise - again like Demeter - she spoke to none until there approached the well the handmaidens of the queen, whom she greeted kindly. 

Braiding their hair, she breathed upon them such a wondrous perfume that when they returned and Astarte saw and smelt the braids she sent for the stranger, took her into the house, and made her the nurse of her child. The great goddess gave the infant her finger instead of breast to suck and at night, having placed him in a fire to burn away all that was mortal, flew in the form of a swallow around the pillar, mournfully chirping. 

But the child's mother, Queen Astarte, happening in upon this scene, shrieked when she spied her little son resting in the flames and thereby deprived him of the priceless boon. Whereupon Isis, revealing her true nature, begged for the pillar and, removing the sarcophagus, fell upon it with a cry of grief so loud that the queen's child died on the spot. 

Sorrowing, then, the two women placed Osiris's coffer on a boat, and when the goddess Isis was alone with it at sea, she opened the chest and, laying her face on the face of her brother, kissed him and wept. 

The myth goes on to tell of the blessed boat's arrival in the marshes of the Delta, and of how Set, one night hunting the boar by the light of the full moon, discovered the sarcophagus and tore the body into fourteen pieces, which he scattered abroad; so that, once again, the goddess had a difficult task before her. 

She was assisted, this time, however, by her little son Horus, who had the head of a hawk, by the son of her sister Nephtys, little Anubis, who had the head of a jackal, and by Nephtys herself, the sister-bride of their wicked brother Set. 

Anubis, the elder of the two boys, had been conceived one very dark night, we are told, when Osiris mistook Nephtys for Isis; so that by some it is argued that the malice of Set must have been inspired not by the public virtue and good name of the noble culture hero, but by this domestic inadventure. 

The younger, but true son, Horus, on the other hand, had been more fortunately conceived - according to some, when Isis lay upon her dead brother in the boat, or, according to others, as she fluttered about the palace pillar in the form of a bird. 

The four bereaved and searching divinities, the two mothers and their two sons, were joined by a fifth, the moon-god Thoth (who appears sometimes in the form of an ibis-headed scribe, at other times in the form of a baboon), and together they found all of Osiris save his genital member, which had been swallowed by a fish. 

They tightly swathed the broken body in linen bandages, and when they performed over it the rites that thereafter were to be continued in Egypt in the ceremonial burial of kings, Isis fanned the corpse with her wings and Osiris revived, to become the rule of the dead.

He now sits majestically in the underworld, in the Hall of the Two Truths, assisted by forty-two assessors, one from each of the principal districts of Egypt; and there he judges the souls of the dead. These confess before him, and when their hearts have been weighed in a balance against a feather, receive, according to their lives, the reward of virtue and the punishment of sin." (Campbell)

We should note that Isis gave the baby her finger instead of her breast to suck and that there was fire involved:

'... The great goddess gave the infant her finger instead of breast to suck and at night, having placed him in a fire to burn away all that was mortal, flew in the form of a swallow around the pillar, mournfully chirping ...'

Possibly I have been influenced by this in coming to believe that the infant morning sun is being fed flames to grow, e.g. in (Qa5-43):

The boat with Isis and the dead Osiris in a coffin landed in the delta of the Nile and it was presumably night and full moon, when Set (a symbol for the dark forces) used his powers to destroy Osiris once more:

'... The myth goes on to tell of the blessed boat's arrival in the marshes of the Delta, and of how Set, one night hunting the boar by the light of the full moon, discovered the sarcophagus and tore the body into fourteen pieces, which he scattered abroad; so that, once again, the goddess had a difficult task before her ...'

"sarcophagus ... stone reputed by the ancient Greeks to consume corpses and hence used for coffins ... stone coffin ... Gr. sárx flesh + phágos -eating ..." (English Etymology)

Marduk won his fight against Tiamat, but Osiris seems rather helpless without his females. Set is male, Tiamat is female - like Hine Nui.

But king Hotu A Matu'a was also rather feeble:

"The ancestors of the present inhabitants came, it is said, from two neighbouring islands known as Marae Renga and Marae Tohio.

Here, on the death of the chief, Ko Riri-ka-atea, a struggle for supremacy arose between his two sons, Ko Te Ira-ka-atea and Hotu-matua, in which Hotu was defeated. (RM:277)" (Routledge according to Barthel 2)

Osiris went into the sarcophagus, the coffin traveled on the water and became a tamarisk, and then the tamarisk became a pillar in a palace, and from that pillar the coffin emerged again. During the return voyage the coffin was opened and Osiris emerged to life again. This is the main story, how the sun temporarily dies to emerge in the east full of life next morning. Certainly we should expect some echo of this grand old myth in the rongorongo day calendars.

Maybe the little night canoe at bottom right in Qa5-28

is a reflection of the 'flesh-eating' coffin floating away?

The return voyage seems to be more stately and like that of a true king (Qa5-37):

In Qa5-30

the little canoe may have changed into a nut (the dry stage prior to tama, the shoot).

The 'nuku' (GD69) appendix has two 'eyes' and maybe therefore is the reflection in the middle of the night of the noon fully grown 'man' (GD15):

The 'peak' of the head is higher in GD15 than in this variant of GD69, and the missing lower part of the body in GD69 may signify sun is in its dark period ('night').

At dawn the kuhane of Hau Maka trampled the bamboo staff of night under her feet so it broke. Feet appear when light is returning.