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Beginning with "October 20 (293) and counting 13 days ahead we will reach Heka:

Ga1-7 Ga1-8 Ga1-9 Ga1-10
no star listed (71) no star listed (72) Hassaleh (73.6) Almaaz (74.7), Haedus I (74.8)
May 31 (151) June 1 2 3 (520)
'May 4 (490) 5 (125) 6 7
"April 20 (*30) 21 (111) 22 (478) 23
Tail-6 ι Ophiuchi (255.3), Grafias (255.4) κ Ophiuchi (256.2), ζ Arae (256.5), ε Arae (256.8), Cujam (256.9) no star listed (257)
Wei, η Arae (254.3), DENEBAKRAB (254.7)
November 30 (700) December 1 (*255) 2 (336) 3
'November 3 (673) 4 (308) 5 6 (*230)
"October 20 (293) 21 22 23 (*216)
Ga1-11 Ga1-12 Ga1-13 Ga1-14
Haedus II (75.9) 5h (76.1) μ Leporis (77.6)  ĸ Leporis (78.0), Rigel (78.1), Capella (78.4), ο Columbae (78.8)

Thuban

ε Leporis (76.0), Cursa (76.4), λ Eridani (76.7)
June 4 5 6 (157) 7 (524)
'May 8 (128) 9 (495) 10 11
"April 24 (480) 25 (115) 26 (*36) 27 (*403)
17h (258.7) Mula-19 Nodus I (260.0), π Herculis (260.7), Ras Algethi (260.8)  Sarin (261.0), ο Ophiuchi (261.4)

Alrisha

no star listed (258) Sabik (259.7), η SCORPII (259.9)
December 4 5 (*259) 6 (340) 7 (707)
'November 7 8 (678) 9 (*233) 10 (314)
"October 24 25 26 (665) 27 (300)
Ga1-15 Ga1-16 Ga1-17 Ga1-18 Ga1-19
λ Leporis (79.6)

Arcturus

Bellatrix, Saif al Jabbar (80.7), Elnath (80.9) Nihal (81.7) Mintaka (82.4), ε Columbae (82.6) Al Hak'ah-3 / Mrigashīrsha-5 / Turtle-20
Arneb (83.0, φ¹ Orionis (83.1), HEKA (83.2), Hatysa (83.5), φ² Orionis (83.6), Alnilam (83.7)
June 8 9 (160) 10 (*81) 11 (528) 12
'May 12 13 (499) 14 (*54) 15 16 (136)
"April 28 29 (485) 30 (120) "May 1 (*407) 2 (*42)
ξ Ophiuchi (262.2), θ Ophiuchi, ν Serpentis, ζ, ι Apodis (262.4), ι Arae (262.8), ρ Herculis (262.9) β, γ Arae (263.3), κ Arae (263.5), σ Ophiuchi (263.6) Lesath, δ Arae (264.7), Choo (264.9)  Alwaid, Maasym (265.1), Shaula (265.3), Kuma (265.6), σ Arae (265.9)

Hamal

Ras Alhague (266.1), Sargas (266.3), μ Ophiuchi, π Arae (266.5), Nan Hae (266.6),  ι Herculis (266.7)
December 8 9 10 (710) 11 (*265) 12 (346)
'November 11 12 (*236) 13 14 (684) 15 (319)
"October 28 29 (668) 30 (303) 31 (*590) "Nov 1 (*225)

If these 13 days were ruled by Heka, then we maybe could expect also the following 13 days to be ruled by some great star. However, there could also be an 'interregnum' of shorter time:

ARIES:
1 Ashvini β and γ Arietis Horse's head 27 = 8 + 9
wife of the Ashvins Sheratan and Mesarthim April 17 (107)
2 Bharani 35, 39, and 41 Arietis Yoni, the female organ of reproduction 41 = 27 + 14
the bearer  Musca Borealis May 1 (121)
TAURUS:
3 Krittikā M 45 Tauri Knife or spear 55 = 41 + 14
the nurses of Kārttikeya The Pleiades May 15 (135)
4 Rohini α Tauri Cart or chariot, temple, banyan tree 68 = 55 + 13
the red one Aldebaran May 28 (148)
ORION:
5 Mrigashīrsha λ, φ¹, and φ² Orionis Stag's head  83 = 68 + 15
the deer's head Heka June 12 (163)
6 Ardra α Orionis Teardrop, diamond, a human head  88 = 83 + 5
the moist one Betelgeuze June 17 (168)

The Hindu system had 5 following nights to Betelgeuze (α Orionis) whereas the Chinese had only 1 day from Heka (λ Orionis) to Alnitak (ζ Orionis). The Arabs jumped 10 days from Heka directly across the Milky Way river over to Gemini.

The creator of the G text seems to have followed the Chinese pattern with Alnitak (Ana-iva) as a stepping stone just beyond Heka. Then came Betelgeuze (Ana-varu) in the center of a 5-glyph sequence - which stretched to the solstice:

Ga1-20 Ga1-21
Three Stars-21 / ANA-IVA γ Leporis (85.9)

Yang Mun

Heavenly Gate, ν Columbae (84.0), ALNITAK, PHAKT (Phaet) (84.7)
June 13 (530) 14 (165)
'May 17 (530 - 27 - 366 = 137) 18 (*85 - 27 = *58)
"May 2 (*43) 3 (490)
λ Arae (267.1), Girtab, ο Serpentis (267.6) Kelb Alrai, μ Arae (268.1), Kew Ho (268.6), η Pavonis (268.7), Apollyon (268.9)
December 13 (713) 14 (348)
'November 16 (320) 17 (*268 - 27 = *241)
"November 2 (*226) 3 (673)
Ga1-22 Ga1-23 Ga1-24 Ga1-25 Ga1-26
 μ Columbae (86.1), Saiph (86.5), ζ Leporis (86.6) Wezn (87.6), δ Leporis (87.7), Tze (87.9) Ardra-6 / ANA-VARU η Leporis (89.0), Praja-pāti, Menkalinan, Mahashim, and γ Columbae (89.3), η Columbae (89.7) μ Orionis (90.3), χ² Orionis (90.5)
BETELGEUZE (88.3), ξ Columbae (88.5), σ Columbae (88.7)

Zuben Elgenubi

June 15 16 17 (168) 18 (535) 19 (536 - 446 = *90)
'May 19 20 (140) 21 22 (508) 23 (509 - 446 = *63)
"May 4 (*45) 5 (126) 6 (493) 7 8
Muliphen (269.0), Basanismus (269.5), Pherkard (269.9) Ptolemy Cluster (270.5) Rukbalgethi Genubi (271.1), ξ Herculis (271.5), Etamin, ν Herculis (271.7), ν Ophiuchi (271.8) ζ Serpentis (272.4), τ Ophiuchi (272.9) Winnowing Basket-7
18h (273.4)
NASH (273.7), θ Arae (273.8)
December 15 16 (350) 17 18 (718) 19 (*273)
'November 18 19 20 (324) 21 (691) 22 (*246)
"November 3 4 (*229) 5 (310) 6 7 (678)
Ga1-27 Ga1-28
6h (91.3) ξ Orionis (92.5)
ν Orionis (91.4), θ Columbae (91.5), π Columbae (91.6)
June 20 (*91) solstice
'May 24 (*64) 25 (145)
"May 9 (*50) 10 (497)
Zhōngshān (274.0), π Pavonis (274.6) ι Pavonis (275.1), Polis (275.9)

Menkar

December 20 (354) solstice
'November 23 (693) 24
"November 8 (679) 9 (314)

Ga1-29 Ga1-30 Ga2-1
Al Han'ah-4  Furud (94.9) Well-22
 TEJAT PRIOR (93.4), γ Monocerotis (93.5), κ Aurigae (93.6), κ Columbae (93.8) δ Columbae (95.2), TEJAT POSTERIOR, Mirzam (95.4), Canopus (95.6), ε Monocerotis (95.7), ψ1 Aurigae (95.9)
June 22 (173) 23 (540) 24 (175)
'May 26 (512) 27 (513) 28 (*68)
"May 11 (132) 12 (*53) 13 (500)
η Sagittarii (276.9) Purva Ashadha-20
KAUS MEDIUS, κ Lyrae (277.5), Tung Hae (277.7) KAUS AUSTRALIS (278.3), ξ Pavonis (278.4), Al Athfar (278.6)
December 22 (722) 23 (*277) 24 (724)
'November 25 (329) 26 (*250) 27 (331)
"November 10 (*235) 11 (682) 12 (*237)

The last pair of glyphs in the line could explain what happened immediately after the solstice. But we do not know how to translate the Arab Tejat:

"Tejat prior is from Al Tahāyi, an anatomical term of Arabia, by which it was know in early days; a name also applied to stars in the head of Orion." (Allen)

The missing head in Ga1-29 could refer to what happened to Rahu. Light returned from the opening at the neck of his severed head:

... It is believed that this immortal head occasionally swallows the sun or the moon, causing eclipses. Then, the sun or moon passes through the opening at the neck, ending the eclipse ...

Live coals (garahu) from an old fire were used for igniting a new fire:

... Up to the present time, fertility spells for fowls have played an important role. Especially effective were the so-called 'chicken skulls' (puoko moa) - that is, the skulls of dead chiefs, often marked by incisions, that were considered a source of mana. Their task is explained as follows: 'The skulls of the chiefs are for the chicken, so that thousands may be born' (te puoko ariki mo te moa, mo topa o te piere) ...As long as the source of mana is kept in the house, the hens are impregnated (he rei te moa i te uha), they lay eggs (he ne'ine'i te uha i te mamari), and the chicks are hatched (he topa te maanga). After a period of time, the beneficial skull has to be removed, because otherwise the hens become exhausted from laying eggs.