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1. The Sagitta (Arrow) constellation arrives later (and higher up) than the main stars of Sagittarius:

 
Ga8-17 Ga8-18 (222) Ga8-19 Ga8-20
Double Double (283.7), ζ Lyrae (283.8), φ Sagittarii (284.1) Sheliak, ν Lyrae (285.1) Ain al Rami (286.2), δ Lyrae (286.3) Alya (286.6), ξ Sagittarii (287.1), Sulaphat (287.4)
'December 30 (364) '31 'May 24 (144) '25
"October 28 (301) "29 "30 "31 (304)
Ga8-21 Ga8-22 Ga8-23 Ga8-24 Ga8-25
λ Lyrae (287.7), Ascella (287.9), Nunki (288.4)  Manubrium (288.8), τ Sagittarii (289.4) ι Lyrae (289.5), Al Baldah (290.1) Aladfar (291.1) Nodus II (291.5), ψ Sagittarii (291.6), θ Lyrae (291.8)
'May 26 (146) 19h (289.2) '28 '29 '30 (150)
'January 3 (368) '4 '5 '6 '7 (372)
"November 1 (305) "2 "3 "4 "5 (309)
Ga8-26 (230) Gb1-1 Gb1-2 (*295) Gb1-3
Arkab Prior (293.0), Arkab Posterior, Alrami (293.2) Deneb Okab (294.0)   Albireo (295.5)
'May 31 'June 1 (152) '2 '3
'January 8 '9 '10 (375) '11
"November 6 "7 "8 (312) "9
Gb1-4 Gb1-5 Gb1-6 (236) Gb1-7 (*300)
  Sham (297.8) Tarazed (299.3) Altair (300.3)
'June 4 '5 '6 (157) '7
'January 12 (377) '13 '14 '15
"November 10 (314) "11 "12 "13
Gb1-8 Gb1-9 Gb1-10 Gb1-11 (*304) Gb1-12 (242)
  Alshain (301.6)      
'June 8 '9 (160) '10 20h (304.4) '12
'January 16 '17 '18 '19 (384) '20
"November 14 "15 "16 (320) "17 "18

Sham (α Sagittae) is the first star to rise in the Arrow constellation, ca 5 days after α Sagittarii (Alrami). Counted from the 'Eye' of the Archer (Ain al Rami) the distance is 297.8 - 286.2 = ca 12 days. From 'May 24 (144) to 'June 5 (156) there are 12 days.

Time runs from lower to higher right ascension. Reasonably the Arrow must come after the Archer. Although the Wikipedia map has κ¹ and κ² well beyond the 20h line the last Sagittarius stars of any importance ought to be the quartet ω, 59, 60, and 62:

"ω, 4.8; A, 5; b, 4.7; and c, 4, forming a small quadrangle on the hind quarter of the horse, were the τετράπλευρον of Ptolemy, which Bayer repeated in the Low Latin Terebellum, still often seen for these stars. The Standard Dictionary gives it thus, but mentions the components as ω, ...  , b and c.

The Chinese knew this little figure as Kow Kwo, the Dog's Country." (Allen)

The mystery of which star is denoted by A has thereby come close to a solution.

... It [the 19th manzil] was also Al Kilādah, the Necklace; and Al Udhiyy, the Ostrich's Nest, marked by our τ, ν, ψ, A, and ζ; while the space between this and the preceding mansions was designated by Al Bīrūnī as 'the head of Sagittarius and his two locks' ...

It must be 59, 60, or 62. A quick look in Wikipedia reveals 62 = c, 59 = , and indeed 60 = A. How could I have missed it? Easy to recognize are these stars in Hevelius: