There is what I think, then there is what Zen says, then there is what the Zen Masters say.
Now do I think that this person here that is typing this message will be reborn into another body upon the death of this body? Like a reset or a respawn in some computer game?
I would have say, “Not exactly”. The Tibetans say that your ‘essence’ is reborn and they look for certain characteristics of that essence in those born after the death of a Tuku or Rimpochay or a High Lama. I actually had first-hand accounts of those who were engaged with the finding of Lama Zopa rebirh, and listen to what they said about the subject.
Memories are a product of the phenomena-existence and expire when the skandhas have arisen expire..yet the ‘essence’ remains. It is like music, in where perhaps the sheet notes and instruments are destroyed but the tune carries on, perhaps taking a new twist or slightly modified – the core or the essence of the tune remains and is distinctly identifiable. This can repeat infinitely unless stopped.
As to what this ‘essence’ actually is…well I just call it the ‘mental habits’ that one has and may or may not be aware of. These habits have a taste (habilitation) for phenomenal existence and suffering. it is our work, our Practice, to abandon; to relinquish; to renounce these mental habits and end the cycle of suffering.
From my own reading of Japanese Zen and Chinese Ch’an, there is a general belief in rebirth. The Zen masters seem to rarely reference the issue of rebirth, and is not the focus of what they are teaching or discussing.
The Mahayana certainly believes in rebirth, the bodhisattva vows to end it!
Thervadans take the issue of rebirth very seriously. They hope to become a Once-Returner, or an Arhut. Four stages of awakening The Bodhisattva blows all of this apart, and the Mahayana is the diamond cutter that is the most expedient means.
So, all the above is MY Humble Opinion. I do not speak for Zen or for the Zen Masters. I only speak for myself, and this arising of skandhas is a work in progress, so forgive the mess.