One of the most common ways of describing Shakyamuni's insight in the early canons is known as the three knowledges (
tevijja). That is, three things were integral to his realization: the ability to reflect his his manifold past lives, the ability to perceive the passing away away and disappearance of beings and an understanding of how beings pass on according to their actions, and finally, the seeing with direct knowledge (
abhinna) that that he has destroyed all negativity.
So , therefore, rebirth was a critical dimension of enlightenment. Although one of the difficulties in talking about rebirth is that we can assume the erroneously thinking notion of a permanent self that is reborn. Where there is a conditioned relationship between one life and the next - one being dying another reborn. The relationship is not one of absolute identity, or difference, but of conditioned arising.
It's better to think in terms of the inheritors of a particular genetic disposition (karmic) rather than physical - although being analogous to our physical being. In discussion like this it's easy to take a non Buddhist position that there is an unchanging essence (reincarnation) that is manifest from lifetime to lifetime - an identity that carries on from one life to the next: "I Will Surive."
Rebirth on the other hand, rather than being likened to a string of beads on which each life is linked to the next on the same thread, is more like a pile of coins with each one stacked on the next, and conditioned by its place in the pile - by what has gone before - but with no unchanging thread connecting them.
The problem with such evidentially scant and unbiased hypothesis concerning the original question posed, is that we lose sight of the world that we are building around us according to our habits and how we confront the challenges of everyday life. Speculation around rebirth - as interesting as that is - should not become a distraction from our fundamental responsibilities in the very present - the way in which we live our lives now.