4. The sacrifice of Berenike's golden tresses could have taken place at the heliacal rising of the Bull's Eye star (ε Tauri), because 136 days later it (Ain) will culminate at midnight (and at Ga5-28):

120
Gb8-30 (1) Ga1-1 Ga1-2 (475) Ga1-3 Ga1-4 (*69)
Hyadum II (473.2)   Ain, θ¹ Tauri, θ² Tauri (474.7)   Aldebaran (477.2)
May 25 26 27 28 29
Ga5-15 (126) Ga5-16 (**99) Ga5-17 (*192) Ga5-18
Algorab (189.5), Gacrux (189.7), Kissin, γ Muscae (190.0), Avis Satyra (190.3) Asterion (190.5), Kraz (190.7), α Muscae (191.2) χ Virginis (191.7), ρ Virginis (192.4),  Porrima (192.5)  β Muscae (193.5)
    Atiks, Rana The Pleiades
September 27 (270) 28 29 30
Ga5-19 (130) Ga5-20 Ga5-21 (*196) Ga5-22 (133) Ga5-23
Mimosa (193.9)   31 Com. Ber. (195.3), ψ Virginis (195.5), Alioth (195.8), Minelauva (196.1), Cor Caroli (196.3)   δ Muscae (197.5)
  Menkhib Zaurak    
October 1 (274) 2 3 4 13h = 197.8
Ga5-24 Ga5-25 (136) Ga5-26 Ga5-27 Ga5-28
  Apami-Atsa (199.5), Diadem (199.9) σ Virginis (201.4)   Mizar (203.4)
Beid Hyadum I Hyadum II   Ain
6 7 (280) 8 9 10
Ga5-29 (140) Ga5-30 Ga6-1 (*206) Ga6-2 Ga6-3 (144)
Alcor, Spica (203.7)   Heze (206.0)    
October 11 12 13 14 15 (288)

Mizar (ζ) and Alcor (80) are close together in Ursa Major as if forming a gateway. And Alcor is rising exactly at the same time as Spica (Ana-roto).

The beginning of the fortnight which ends at Mizar (which is rising heliacally in day 10 in month 10) comes with Kissin (and a host of other stars). A further 5 days are needed to reach day 288 (twice 144), and in the center is Heze (ζ Virginis).

I guess Ain could be the whirlpool into which an arrow was shot in order to bring fire to the shore:

... A man had a daughter who possessed a wonderful bow and arrow, with which she was able to bring down everything she wanted. But she was lazy and was constantly sleeping. At this her father was angry and said: 'Do not be always sleeping, but take thy bow and shoot at the navel of the ocean, so that we may get fire.'

The navel of the ocean was a vast whirlpool in which sticks for making fire by friction were drifting about. At that time men were still without fire. Now the maiden seized her bow, shot into the navel of the ocean, and the material for fire-rubbing sprang ashore. Then the old man was glad. He kindled a large fire, and as he wanted to keep it to himself, he built a house with a door which snapped up and down like jaws and killed everybody that wanted to get in.

But the people knew that he was in possession of fire, and the stag determined to steal it for them. He took resinous wood, split it and stuck the splinters in his hair. Then he lashed two boats together, covered them with planks, danced and sang on them, and so he came to the old man's house. He sang: 'O, I go and will fetch the fire.' The old man's daughter heard him singing, and said to her father: 'O, let the stranger come into the house; he sings and dances so beautifully.'

The stag landed and drew near the door, singing and dancing, and at the same time sprang to the door and made as if he wanted to enter the house. Then the door snapped to, without however touching him. But while it was again opening, he sprang quickly into the house. Here he seated himself at the fire, as if he wanted to dry himself, and continued singing. At the same time he let his head bend forward over the fire, so that he became quite sooty, and at last the splinters in his hair took fire. Then he sprang out, ran off and brought the fire to the people.

If Ain was the navel of the ocean, then the navel of the earth (Te Pito O Te Kainga) ought to be on the opposite side, close to Antares.