3. Flamsteed suggests, it seems, in his Atlas Coelestis that Orion could be the father:

"Eridanus streams away from the left foot of Orion, as described by the ancient Greek astronomer Ptolemy, in this chart from the Atlas Coelestis of John Flamsteed. Flamsteed was scrupulous about following the descriptions given by Ptolemy in his Almagest.

In his list of stars in Orion, Ptolemy said that the 'bright star in the left foot' of Orion, which we know as Rigel or Beta Orionis, was common with Eridanus. However, he did not repeat this description in his star list for Eridanus (which he simply called potamos, or river). Instead, Ptolemy said that the river began with 'the star after the one in the foot of Orion', which we now know as Lambda Eridani. Lambda Eridani can be seen just below right of Rigel on Flamsteed’s chart, above. The star next to the shin of Orion marked ‘h’ on this chart is the one we know as Beta Eridani."

Ian Ridpath (http://www.ianridpath.com/startales/startales3.htm) does not comment upon the 'erigated' sword handle. His statement that Ptolemy had the beginning of the River at λ Eridani does not necessarily imply Ptolemy meant its water flowed away from the left foot of Orion, it could be only a reference to where the constellation Eridanus began. However, Ptolemy may have left us a Sign in mentioning not only β Orionis but also λ Eridani as belonging in the River, with β Eridani perhaps like a hua reva, in which case Eridanus indeed would run towards stars with lower right ascension numbers - time would run withershins. Notably the left shin of Orion is uplifted.

λ Eridani could be at ariki in Ga1-13 (cfr at Beid and Theemin), is a day of Mars and just before 'Rahu':

There is no mata visible and the letter is λ, therefore Ga1-13 could illustrate the 'father' of atariki in Ga1-24, 11 ('one more') days later.

We ought to list also η Orionis, the star at the top of his sword handle. A handle (like a sword) must be a male sign because a hand (like a piece of cloth) is female.

"... occasionally and very appropriately [η] has been designed Saiph, from Saif al Jabbār, the Sword of the Giant ..." (Allen)

Today Saiph is the name for  ĸ Orionis, at his right foot.