Using the element argument, let's explore that a little further:

We know the primals each represent an element

Fire = Ifrit
Wind = Garuda
Ice = Shiva

etc
but what of darkness and light, or unbral and astral.

Well, this is what I came up with:
Bahamut to me seems like he's a Darkness primal. He causes death, destruction, sickness, etc. Things attributed to darkness or evil.

Arcanists can summon Carbuncle. That leads me to believe he/she's a primal. Could be ours.

Now, looking even further, we know Odin and Fenrir exist. Should we consider them primals? If so, which element to they represent? I think Fenrir obviously is darkness, and same with Odin. Odin represents death/underworld, similarly to Bahamut.

But now, we have an issue...There are 3 umbral primals (Bahamut, Odin, Fenrir) but only one Astral primal (Carbuncle). Knowing SE, one of the themes here will be balance, so if there are 3 umbral primals, what are the other 2 astral primals?

As was mentioned before, Alexander would most likely be an Astral primal, but we're still short one.

Umbral Primals:
Bahamut
Odin
Fenrir

Astral Primals:
Carbuncle
Alexander?
???