There is a pair of 10 for each kind of bird and there is also a pair of names (Teke and Oti) for each bird name. For Sun time was measured up to 10 only, presumably because there are no more fingers. Moon has 2 'legs', though. And Easter Island lies out of the reach for zenith Sun.

Wordplay can construct teke as something else (ke) than teka (the 'dart of fire'). I.e. Waxing Moon could have been named te-ke.

Oti is very similar to koti:

Koti

Kotikoti. To cut with scissors (since this is an old word and scissors do not seem to have existed, it must mean something of the kind). Vanaga.

Kotikoti. To tear; kokoti, to cut, to chop, to hew, to cleave, to assassinate, to amputate, to scar, to notch, to carve, to use a knife, to cut off, to lop, to gash, to mow, to saw; kokotiga kore, indivisible; kokotihaga, cutting, gash furrow. P Pau.: koti, to chop. Mgv.: kotikoti, to cut, to cut into bands or slices; kokoti, to cut, to saw; akakotikoti, a ray, a streak, a stripe, to make bars. Mq.: koti, oti, to cut, to divide. Ta.: oóti, to cut, to carve; otióti, to cut fine. Churchill.

Pau.: Koti, to gush, to spout. Ta.: oti, to rebound, to fall back. Kotika, cape, headland. Ta.: otiá, boundary, limit. Churchill.
Oti

To come to an end; to suffice, to be enough: ku-oti-á, it is finished; ina kai oti mo kai, there is not enough to eat; he-oti á, there isn't anymore left, it's the last one; it's enough with that. Vanaga.

Ta.: 1. Oti, presage of death. Sa.: oti, to die. 2. To cut. Mq.: koti, oti, id. Sa.: 'oti, id. Ma.: koti, id. Churchill

The 'death' of Moon surely must be at the end of the waning phase.

The order of the Month is waxing followed by waning, i.e. teke - oti. Each bird name in the list represents a month and therefore a Teke. a Oti.

The parent birds (manu tara.erua) do not partake in the cycle of waxing and waning. Not until they have produced offspring can the spring light come.