Once again. It was hardly a coincidence that the triplet of 'walking skies' together covered 48 right ascension days, because the creator of the H text surely must have thought of and used this well known and elementary number of ancient constellations visible in the night sky (ragi) in order to 'underline' his idea of demonstrating the effects of the precession as perceived for the northern spring equinox:
 
APRIL 5 6 (96 = 80 + 16)
June 8 (159) 9 (96 + 64, *80)
Ga1-15 Ga1-16
ARCTURUS (α Bootis)  ELNATH (*80)
1b   2b   3b
Hb3-16 (116) Hb3-41 (141) Hb4-16 (163)
ELNATH (*80)    
APRIL 6 (96 = 80 + 16)    
48

... Ptolemy scientifically followed with those now known as the ancient forty-eight, in the 7th and 8th books of the Syntaxis, twelve of the zodiac with twenty-one northern and fifteen southern, made up by 1028 [= 2 * 514] stars, including 102 αμόρφωτοι, all probably from Hipparchos, although with some acknowledged alterations by himself ..
 

The distance from Hb3-16 to Hb3-41 is 141 - 116 = 25 glyphs (right ascension days). This should correspond to moving from Ga1-16 to glyph number 16 + 25 = 41 in the G text.

APRIL 6 (96) + 25 = 121 (MAY 21). Here we can perceive a beginning of an explanation for my suggestion that Hb3-41 could refer to Bharani (41 Arietis).

In the era of Bharani this star would have risen in the east (truly heliacally and together with the sun) at 0h in day 121 (May 21) - 41 = 80 ("March 21 according to my convention for documenting ancient dates).

In the G text we have to look 64 - 41 = 23 right ascension positions earlier than Hyadum II in the Golden Age of the Bull and 80 - 41 = 39 right ascension positions earlier than Elnath (notice the tiny dot for drawing attention):

FEBR 26 (57, 422) *39 APRIL 6 (96)
Gb4-22 Ga1-16
BHARANI (*41)  ELNATH (*80)
May 1 (121, *41) June 9 (160, *80)
"March 21 (0h, *365) "April 29 (119, *39)

And in the G text we can find a hint of this day number in the Golden Age of the Bull, because FEBRUARY 26 (31 + 26 = 57) is day number 365 + 57 = 422 counted from JANUARY 1 in the previous year → Gb4-22.

But in the H text we have to move ahead with 25 (= 141 - 116) positions, which will bring us to the place corresponding to Ga2-11 (41) at MAY 1 (*41).

FEBR 26 (422)

*39

 APRIL 6 (96)

'25

 MAY 1 (121, *41)

Gb4-22

Ga1-16

Ga2-11 (16 + 25)
BHARANI (*41)  ELNATH (*80) NUNKI (*288.4)

The 'fish-hook' suggests a place out at 'sea', and in MAY 1 (in the Golden Age of the Bull) the star Nunki (*288.4) would ideally have been at the right ascension line at the Full Moon in the night. Elnath (*80) + *25 = *105 and this was the position of the Sun. By adding 366 / 2 = 183 days the ideal position of the Full Moon would be found to be *288.

... This [σ Sagittarii] has been identified with Nunki of the Euphratean Tablet of the Thirty Stars, the Star of the Proclamation of the Sea, this Sea being the quarter occupied by Aquarius, Capricornus, Delphinus, Pisces, and Pisces Australis. It is the same space in the sky that Aratos designated as Water ...

In that part of the H text we are here currently studying, however, there is no direct sign (as far as I can see), which could suggest a point where daytime will change into night time. Instead the 'walking' (loco-motion) is progressing without interruption.

Therefore I suggest the star in the Golden Age of the Bull at Hb3-41 should be ω Gemini (*105.4 = *288.4 - *183.0).

1b *25 2b   3b
Hb3-16 (116) Hb3-41 (141) Hb4-16 (163)
ELNATH (*80) ω Gemini (*105.4)  
APRIL 6 (96 = 80 + 16) MAY 1 (*41)  
"April 29 (119, *39) "May 24 (144)  
June 9 (160, *80) July 4 (185)  
48

... Ptolemy scientifically followed with those now known as the ancient forty-eight, in the 7th and 8th books of the Syntaxis, twelve of the zodiac with twenty-one northern and fifteen southern, made up by 1028 [= 2 * 514] stars, including 102 αμόρφωτοι, all probably from Hipparchos, although with some acknowledged alterations by himself ..

Of all the stars rising with the sun in MAY 1 ("May 24, July 4) I have here chosen ω Gemini (*105.4) because this was the only star with the correct fraction .4 in order to calibrate the Sun calendar with Bharani (*41.4 = *105.4 - *64.0).

No wonder July 4 (a place for birth) was chosen as the Day of Independence, it was a reflection (so to say) of the time for Beltane in the Golden Age of the Bull (the day which currently coincided with the heliacal place of Bharani, *41 = *105 - *64).