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5. Looking quickly in my book I can find only 3 stars in the region around 16h, all of them in the Scorpion:

Dschubba δ Scorpii 22º 29' S 15h 57m 242.7 178.7
Acrab β Scorpii 19º 40' S 16h 03m 244.3 180.3
Lesath ν Scorpii 19º 20' S 16h 09m 245.8 181.8

Counting Gb8-30 twice will not put Dschubba at Ga7-7, but by counting it only once can we get it to be at  Ga7-10:

†173
Ga7-5 Ga7-6 Ga7-7 (†240) Ga7-8 Ga7-9 Ga7-10 (†243)
Ga7-9 Ga7-10 (†243)
Dschubba (?)

There is another possibility. The star π Scorpii, not listed in my book, is rising slightly earlier than Dschubba and its letter π invites us to count:

Vrischika π Scorpii 26º 07' S 15h 58m 51.12s *15h 56m *241.7 *177.7
Dschubba δ Scorpii 22º 29' S 16h 00m 20.01s 15h 57m 242.7 178.7

Using information from Wikipedia it is possible to calculate the distance from Vrischika to Dschubba as (16 * 60 * 60 + 20.01) - (15 * 60 * 60 + 58 * 60 + 51.12) = 57620.01 - 57531.12 = 88.89 seconds = 1m 29s.

The letter π and the fact that it today is drawn to be the first of the Scorpion stars which delineate the figure should make us use Vrischika as the sign of the 'birth' of Scorpion:

†173
Ga7-5 Ga7-6 Ga7-7 (†240) Ga7-8 Ga7-9 Ga7-10 (†243)
Ga7-8 Ga7-9 (†242)
Vrischika (?)

Had we counted puo in Gb8-30 twice Vrischika would come one step earlier. These results could seem to favour our traditional way to count, i.e. to count puo in Gb8-30 twice. There will then be 240 days from Rogo in Gb6-26 up to and including ariki in Ga7-6. Counted from Achernar there will be 216 days:

Achernar α Eridani 0.45 57º 29' S 01h 36m 24.3 432.3
40 174
Ga7-5 Ga7-6 (*240)
Gb7-21 (*24) 214

However, from the birth of Sun (presumably at Gb7-22) he maybe should be present during 214 days (100 less than 314). On the other hand, the ariki glyphs were probably signs for finals (cfr at Tagaroa).

We can calculate the distance from Achernar at 01h 37m 42.75s to Vrischika as (15 * 60 * 60 + 58 * 60 + 51.12) - (1 * 60 * 60 + 37 * 60 + 42.75) = 57531.12 - 5862.75 = 51668.37 seconds = 14h 21m 8.37 seconds.

This can be converted into days (and glyphs) by dividing the number of minutes by 4, i.e. (14 * 60 + 21 + 8.37 / 60) / 4 = 861.14 / 4 = 215.3 days. With Achernar at day number 24.3 we will therefore have Vrischika at day number 24.3 + 215.3 = 239.6:

Ga7-5 (175) Ga7-6 (*240)
Vrischika (?)

This is an acceptable solution, I think. Vrischika is the first part of the Scorpion and Sun cannot be there.