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I can perceive a sequence of 4 glyphs beyond Gb2-1, followed by 6 more:

Gb1-26 Gb2-1 (256)
DECEMBER 1 2 (336)
21h (319.6) χ Capricorni (320.0), ν Aquarii (320.3), γ Equulei (320.6), ο Pavonis (320.8)
Armus (319.0), Dorsum (319.3), Tsoo (319.7)
February 3 4 (400)
'January 7 (372) 8
Christmas Eve "December 25 (359)
NAKSHATRA DATES:
JUNE 2 3 (154)
9h (137.0) no star listed (138)
σ¹ Ursa Majoris (137.0), κ Cancri (137.3), τ Cancri (137.4), Alsuhail (137.5), σ² Ursa Majoris (137.6), τ Ursa Majoris (137.7), ξ Cancri (137.8)
August 5 6 (218)
'July 9 10 (191)
"June 25 26 (177)
Gb2-2 Gb2-3 Gb2-4 Gb2-5 (260)
DECEMBER 3 4 5 6 (340)
δ Equulei (321.7), φ Capricorni (321.8) Kitalpha (322.0), Alderamin (322.9) Dai (323.5), β Equulei (323.8) γ Pavonis (324.1), Yan (324.6)
February 5 6 7 (403) 8
NAKSHATRA DATES:
JUNE 4 5 6 (157) 7
π Cancri (139.2), Miaplacidus (139.3), Tureis (139.8) no star listed (140) Markab Velorum (141.5), Al Minhar al Asad (141.6) Star-25

ANA-HEU-HEU-PO

ALPHARD (142.3), ω Leonis (142.6), τ¹ Hydrae (142.7)
August 7 8 9 10 (222)
Gb2-6 Gb2-7 Gb2-8 (263) Gb2-9 Gb2-10 Gb2-11
DECEMBER 7 8 9 10 11 12 (346)
Al Sa'd al Su'ud-22 / Emptiness-11 no star listed (326) Castra (327.2), Bunda (327.5)

Sirius

Nashira (328.0), Azelfafage, κ Capricorni (328.7) Enif, Erakis (329.2), 46 Capricorni, Jih (329.3), ι Piscis Austrini (329.4), λ Capricorni (329.6), ν Cephei (329.7), Deneb Algiedi (329.8) θ Piscis Austrini (330.1)
Tsin (325.2), Alphirk (325.7), SADALSUD, ξ Gruis (325.9)
BUNDA (Foundation) / KAKKAB NAMMAΧ (Star of Mighty Destiny)
Februay 9 10 (41) 11 12 (408) 13 14 (45)
NAKSHATRA DATES:
JUNE 8 9 (525) 10 11 12 13 (164)
Al Tarf-7 A Hydrae (144.1)

Vega

Ukdah (145.4), κ Hydrae (145.5), Subra (145.8) ψ Leonis (146.4), Ras Elaset Australis (146.6) Vathorz Prior (147.9) υ¹ Hydrae (148.4), Ras Elaset Borealis (148.7)
ψ Velorum (143.3), ALTERF, τ² Hydrae (143.4), ξ Leonis (143.5)
August 11 12 13 14 15 16 (228)

... β and ξ also constituted the Persian lunar station Bunda and the similar Coptic Upuineuti, the Foundation; but β alone marked the sieu Heu, Hiu, or , Void, anciently Ko, the central one of the seven sieu which, taken together, were known as Heung Wu, the Black Warrior, in the northern quarter of the sky. It is found in Hindu lists as Kalpeny, of unknown signification. On the Euphrates it was Kakkab Nammaχ, the Star of Mighty Destiny, that may have given origin to the title of the manzil [Al Sa'd al Su'ud], as well as to the astrologers' name for it - Fortuna Fortunarum ...

My intuition says we should try to count 20 days back in time. Gb2-5 (260) - 20 = 240 (Gb1-11):

Gb1-9 Gb1-10 Gb1-11 Gb1-12 Gb1-13 (242)
NOVEMBER 14 15 16 (320) 17 18
ε Pavonis, θ Sagittarii (302.3), γ Sagittae (302.5), μ Pavonis (302.7) τ Aquilae (303.8) 20h (304.4) Shang Wei (305.2), θ Sagittae (305.4), Tseen Foo (305.6), ξ Capricorni (305.8) Tso Ke (306.3)
η Sagittae (304.2), δ Pavonis (304.4)
January 17 18 (383) 19 20 21
NAKSHATRA DATES:
MAY 16 17 (137) 18 19 20
ω Cancri (120.2) 8h (121.7) ρ Puppis (122.0), Heap of Fuel (122.1), ζ Monocerotis (122.3),  ψ Cancri (122.6), Regor (122.7) Tegmine (123.3) Al Tarf (124.3)

Ras Algethi

χ Gemini (121.0), Naos (121.3)
July 19 (200) 20 21 22-7 23

And then to return by adding 20 nights to for instance Gb1-17 (246):

 
Gb1-14 Gb1-15 Gb1-16 Gb1-17 (246) Gb1-18 Gb1-19
NOVEMBER 19 20 21 22 (326) 23 24
Gredi (307.2), σ Capricorni (307.5), Alshat (307.9) Al Sa’d al Dhabih-20 / Ox / Herd Boy-9 Okul (309.6), Bos (309.9)

Arneb

ο Capricorni (310.2), θ Cephei (310.5)

Alnilam

Rotten Melon, φ Pavonis (311.2), η Delphini (311.4), ζ Delphini, ρ Pavonis (311.7)

Phakt

Rotanev, ι Delphini (312.3), τ Capricorni (312.6), κ Delphini (312.7), SVALOCIN, υ Capricorni, υ Pavonis (312.8)
DABIH (308.0), κ Sagittarii (308.1), Sadir (308.4), Peacock (308.7)
January 22 23 24 25 (390) 26 27
NAKSHATRA DATES:
MAY 21 22 23 24 (144)   25 26
χ Cancri (125.2), Bright Fire (125.4) Avior (126.4), φ Cancri (126.8) ο Ursa Majoris (127.4)  Pushya-8 Āshleshā-9 / Willow-24 Al Nathrah-6
υ Cancri (128.1), θ CANCRI (128.2), η Cancri (128.5) π¹ Ursa Majoris, δ HYDRAE (129.6), Al Minhar al Shujā, Museida (129.9)

Ras Alhague

BEEHIVE (130.4), Xestus (130.5), Ascellus Borealis (130.9)
July 24 25 26 27 (208) 28 29
CANCER:
8 Pushya γ, δ, and θ Cancri Cow's udder, lotus, arrow and circle  128 = 113 + 15
the nourisher Beehive July 27 (208)
HYDRA:
9 Āshleshā δ, ε, η, ρ, and σ Hydrae Serpent 130 = 128 + 2
the embrace Uninhabited Spot July 29 (210)

20 seems to have been the number of nights in a Moon month.

... The Gilbert Islanders are Polynesians, having emigrated, according to their traditions, from Upolu, Samoa, which they look upon as te buto (Maori pito), the Navel of the World. They never counted the nights of the Moon beyond the twentieth, so far as Grimble was able to ascertain, and in the vagueness of their lunar calendar bore no resemblance to their Micronesian neighbors of the Carolines ...

The Babylonians counted with 18 lunar stations in the night, together amounting to 18 * 20º = 360º: