Jeanne Reames wrote:I don't think it's either one. Not sure why Waldemar thinks so.* This is a case of "looking for famous people in every image..."

Now, one can make a pretty decent case that the lion-hunt mosaic has Alexander in petasos (hat) on the left, and Krateros running up to save him on the right, based on the reference to a famous sculpture commissioned by Krateros's son after his death. But this mosaic? There's no reason at all to assume either of these figures are anybody we can name.
(*He also has now argued the Alexander Sarcophagus doesn't depict Issos, but another battle, and I disagree on that assignment, as well. I still find Issos the most likely choice.)
Whenever I come across Alexander's pretended likenesses, they do give me headaches. Any Apollo is always "Alexander". But some indeed give one food for thought.
This mosaic is interesting, because the petasos is also there (flying away, which gives me goose pimples everytime I see this ultra "modern" artistic subtlety).
Well -- both mosaics were found in Pella archaeological site. The young man in both mosaics wear (or at least one was wearing it before the thing flew away) petasos. Of one of them, as you said, a good case could be brought on. So why not the other hatted figure as well? It could be a jolly coincidence, ok, but in both mosaics only one figure wears the hat. Because probably Alexander was seen wearing it often (is it written somewhere?), so it was like a brand when he was not wearing battle stuff. That hat very very probably links to Alexander then.
But what calls my attention there is the double ax, really. I don't have the time (or the resources) to go after it, but I'd like to check for double ax in hunts in Northern Greece. Or in mainland Greece at least. To check if that was a common hunt weapon. I think it too heavy for hunts... But these are conjectures.
Things is: the double ax is Hephaistos' attribute -- a long, doubled-headed ax, as they say. And that other guy had a very similar rooted name as of the god.
Ήφαιστος , the god
Ἡφαιστίων , the general
Ήφαιστeίoν, the temple in Athens (here not sure how they speel it in Attic)
I have wee notions of linguistics/etimology, I know roots are as weird as they go. A word can be so similar, but if you go checking the root, it is something else. Specially when Hephaestion's name has a 'w', and not an 'o'.
I found something about the god's name and the temple's:
"The question of the origin of the god [Hephaistos] is destined to remain largely open because the evidence that he was present in the pantheon of the Mycenaean age is based solely on a tablet from Knossos dated to the fourteenth century B.C.E. This mentions the word
a-pa-i-ti-jo which, it has been proposed, may correspond to Hephaistos or Hephaistion , that is “sacred to Hephaistos”. (M. Barbanera, 2013)
A second thing: Γνῶσις. If we read Γνῶσις as the obvious "knowledge", wouldn't it be nice to think that it means: "Knowledge made me"? Like: made as per actual knowledge of people involved? Now, that'd be terrific!!
It'd be grand to have a real portrait of Alexander and Hephaistion, or at least the intention would be there anyway. *Aaand* from their birthplace and from their era wow!
But well, who knows...

Come live forever with me, or transpire / a flame alone on a funeral pire / We'll build an empire if we so desire, travel the world, and set it on fire.