I feel its first appearance as the Cloud of Darkness largely explains what the Void is since CoD is pretty much a physical manifestation of it, but I get the impression that the Void is largely the primordial state of the universe, which is trying to undo the Order that has created the worlds we know.

How the Void is sentient is beyond me, perhaps a side effect of Order giving it a will but who is to say. The Void existed in the early games as a true balance to change the dynamics of good and evil. Its like the Nothingness in Kingdom Hearts in that matter, but its only been in recent years that the Void has really been brought in as some kind of story element though I don't necessarily feel all of them are connected, so I don't think the Void of FFV is the same as the Void from the Ivalice titles, or the ones from FNC XIII titles. They may share similar themes but I highly doubt someone at SE is actually trying to write in some grand mythology.