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Possibly January 19 - i.e. day 384 > 13 * 29½ and on average the coldest day in the northern hemisphere - was the first day of a new season. The inoino glyph has a triplet of mata in front:

Shaula 11 12 13 (244) Al Naam 1 2 3
January 13 14 15 16 17 18 (383)
Ca11-14 Ca11-15 Ca11-16 (300) Ca11-17 Ca11-18 Ca11-19
tupu toona rakau i te vai te moko te marama te kava ihe manu kara etahi te mauga e hiku hia
Sham (297.8) Tarazed (299.3) Altair (300.3) ι Sagittarii (301.2), Terebellum (301.3) Alshain (301.6), ε Pavonis, θ Sagittarii (302.3) μ Pavonis (302.7)
July 15 16 17 18 19 (200) 20
Heka 7 8 9 10 (63) 11 12
σ Gemini (115.7), Pollux (116.2) Azmidiske (117.4) no star listed χ Carinae (119.9) Naos (121.3)
Al Naam 4 5 6 (250)
January 19 20 (385) 21
Ca11-20 Ca11-21 Ca11-22
te inoino te hokohuki te moko
 ξ Capricorni (305.8) Gredi (307.2), σ Capricorni (307.5) Alshat (307.9), Dabih (308.0), κ Sagittarii (308.1), Sadir (308.4)
July 21 22 23 (204)
Heka 13 Alhena 1 2 (68)
Heap of Fuel (122.1) Regor (122.7), Tegmine (123.3) Al Tarf (124.3)

If qualities adhere to numbers, then manzil day 249 (Al Naam 5) ought in some way to resemble November 25 (329) when Antares rose heliacally, because this was RA day 249.

The last Archer star is κ, appropriately in the tail of the horse, and it rose in manzil day 250 (Al Naam 6).

I believe the letter κ - said once to have illustrated a hand (Chikin and Blood Moon comes to mind) - was used systematically to indicate the transfer from one constellation figure to the next. I have suspected this since observing the close proximity in time between κ Aurigae and Tejat Prior, the last star in Auriga respectively the first (Greek lettered star) in Gemini. Notably Castor has a bow and arrow:

Albatain 10 11 (403) 12  13 (40)
June 22 23 (St John's Eve) 24 (St John's Day)  25
Ca4-17 Ca4-18 (94) Ca4-19 Ca4-20
te hau tea tupu te rakau - te henua te hau tea tupu te rakau
 Tejat Prior (93.4)  κ Aurigae (93.6) Furud (94.9), Tejat Posterior, Mirzam (95.4) Canopus (95.6)

Metoro said tupu te rakau at the left part of Ca4-18, which is being inserted in (ki roto ki) the henua part. This happened in manzil day 403 (= 181 + 182), a number which suggests the day when Sirius was in its nakshatra position (because June 30, day 181, was its heliacal position).

Therefore Gredi (α Capricorni), see Ca11- 21, could (structurally seen) correspond to the left front toe of Castor, i.e. marking an important new point (tara) in time - because κ Sagittarii followed the next day.