A map shows Tepeu located on the western coast (close to the end of the kuhane journey):
 
 
Tuu Ko Ihu buried the head of the sun (god), i.e. he did exactly the opposite of hanging the skull high in his house. If we accept a view of the sacred geography where midsummer 'is equal to' Poike in the east, then a hole (meaning the lowest point) ought to be found in the west.
 
Tepeu surely is Te Peu and among the meanings of this word we find 'persons stooping with age', 'housebeams sagging under weight':
 
Peu

1. Axe, adze, mattock; peu pakoa, an axe poorly helved. 2. Energy. Peupeu: 1. To groan. 2. To be affectionate, to grow tender; peupeuhaga, friendship. Mq.: pèèhu, haápeéhu, pekehu, to make tender. 3. Pau.: peu, habit, custom, manners. Ta.: peu, custom, habit, usage. 4. Pau.: hakapeu, to strut. Ta.: haapeu, id. Churchill.

Sa.: mapelu, to bend, to stoop, to bow down, persons stooping with age, housebeams sagging under weight. To.: pelu, bebelu, to fold, to crease. Fu.: pelu, peluki, to fold. Uvea: pelu, id., mapelu, to bend, to bow. Ha.: pelu, to double over, to bend, to fold. Rapanui: peu, axe, adze. Churchill 2.

When sun stands low in the sky his best time (midsummer) is past.

Another meaning in peu is 'to fold, to crease' - and our thoughts ought to go to the head of a ua club, where the compressed face causes wrinkles at the top. Instead of the long nose in the ao paddle (stretching the face so wrinkles disappear) the short nose is not enough to keep the sky vault high. Ihu means nose, and the creator of the story has given us a sign in the name of Tuu Ko Ihu ('the nose is standing').

Ihu

1. Nose; ihu more, snub nose, snub-nosed person. 2. Ihuihu cape, reef; ihuihu - many reefs, dangerous for boats. 3. Ihu moko, to die out (a family of which remains only one male without sons); koro hakamao te mate o te mahigo, he-toe e-tahi tagata nó, ina aana hakaara, koîa te me'e e-kî-nei: ku-moko-á te ihu o te mahigo, when the members of family have died and there remains only one man who has no offspring, we say: ku-moko-á te ihu o te mahigo. To disappear (of a tradition, a custom), me'e ihu moko o te tagata o te kaiga nei, he êi, the êi is a custom no longer in use among the people of this island. 4. Eldest child; first-born; term used alone or in conjunction with atariki. Vanaga.

1. Nose, snout, cape T (iju G). Po ihuihu, prow of a canoe. P Pau.: ihu, nose. Mgv.: ihu, nose; mataihu, cape, promontory. Mq., Ta.: ihu, nose, beak, bowsprit. Ihupagaha, ihupiro, to rap on the nose, to snuffle. 2. Mgv.: One who dives deep. Ta.: ihu, to dive. Churchill.

Sa.: isu, nose, snout, bill. Fu., Fakaafo, Aniwa, Manahiki: isu, the nose. Nuguria; kaisu, id. Fotuna: eisu, id. Moiki: ishu, id. To., Niuē, Uvea, Ma., Ta., Ha., Mq., Mgv., Pau., Rapanui, Tongareva, Nukuoro: ihu, id. Rarotonga: putaiu, id. Vaté: tus, id. Viti: uthu, nose. Rotumā: isu, id. ... usu and ngusu ... serve as transition forms, usu pointing to isu the nose in Polynesia and ngusu to ngutu the mouth, which is very near, nearer yet when we bear in mind that ngutu the mouth is snout as well and that isu the nose is snout too ... Churchill 2.

The meaning 'axe' etc probably is because the old 'tree' should be felled. 'They lifted the king off to the side and let him fall.' The proper season for this event should be 'fall'.