So to start with let's get this out of the way, I am using the term Eikon to refer to all magical phenomena created as a combination of belief and aether.
The reason I refer to them as such is because of a fundamental lack of understanding of their nature on most people's parts. The term Primal refers to the gods worshiped by the beast tribes, however, as we've seen not only can other being be summoned, but the actual creation is not the summoning of one of their gods to this plane, but merely a form created based on what the summoners believe their god to be like. The creation itself, and I must stress this, has no relation whatsoever to the god itself. Supposing it exists in the first place but theology is a matter for another time.
Something puzzling though is the fact that when resummoned, the Eikon seems to have memories of prior summonings, my current theory is that the belief of it's worshipers acts as a form of memory for it. They know it was defeated by the warrior of light and thus it is created knowing of them.
Another matter is those that seem to be maintained without belief or aether, namely, Odin, Bahamut, and the warring triad. The latter are imprisoned by the Allagans, and thus we can bet that their technology somehow is able to maintain their form and at the same time siphon off the energy they give, how such a mechanism works is beyond me however. Which leaves Odin, I'm unsure how much it siphons aether from the shroud, but it does not seem to be as much as the others, furthermore, it might be able to sustain itself off of the belief of one individual, namely the one that it bonds with to make the rider, taking advantage of the fact that it does no more than exist when not bonded to live off of it's saved up aether.
Thoughts on the matter? Counterpoints? Added arguments?
(For some reason it felt natural to write this in a semi-in character fashion, but by all means don't feel obligated to reply in such a fashion if you don't want to)