But I shall keep looking.
Actually, just found this:
Reincarnation and Buddhism: Here we go again and his text confirms what I have been led to believe by the Perennialists, that the commonly-expressed notion of the self 'getting another chance' is a misunderstanding of the doctrine.
And similarly, having looked into 'what reincarnates in Hinduism' we have
Atman – the principle of selfhood as such, beyond identification with forms, phenomena or individualities; it is the essence of being, and transcends all forms and modes of being personality.
Atman is other than and distinct from the ever-changing individual personality described by
Ahamkara (the egoic self, psychic I-ness, Me-ness, identification of self as an autonomous being, etc.).
Ahamkara is a conglomeration and aggregation of habits, prejudices, desires, impulses, delusions, fads, behaviors, pleasures, sufferings, fears, etc., etc...
Again, it seems to me that when we look at reincarnation, when we see 'A' in 'B', it's stuff passed on much like our dna, much in the way we might resemble a parent or relative, it's not that A is reborn in B (if so, then B would carry on talking where A left off, as it were), it's rather that 'B' inherits the world, microcosm and macrocosm, that A bequeaths to him/her ... and characteristics, traits, actions, tastes, distastes, etc., are all part of that outer psychic shell that can pass via resonance within families and across continents ...
I actually think they're all preaching the same thing: Christ talks about 'the light' and John says "that life was the light of men" (John 1:4).
Life goes on. Atman goes on.
We, on the other hand, that which we constitute as 'ourselves' have our entrances and our exits, and we leave the residue of our passage for those who follow,
but we do not repeat ourselves in another body, nor is our 'me-ness' repeated, given another go round or another bite of the cherry, that, I firmly believe, is a misreading of the doctrines. In all traditions there are the popular and often sentimental expressions of the doctrine, believed in all good faith, but erroneous. An all traditions will find a way of putting off until tomorrow that which needs to be addressed today ...
The aim of Hinduism, Buddhism, Christianity, the aim of all the Great Traditions, is to transcend the individuality, the egoic consciousness, to realise one's true nature which can only be realised by giving up that nature we cling to so religiously as me, my rights, my freedoms, my autonomy, my self-determination, my self-direction,
my individuality ... in realising we are nothing we can realise all that is; in clinging to who we are we blindfold ourselves to everything we could be.
In the end the message is a tough one. I'm sure each tradition has its expression, but the one I know is from my own. Christ to the mystic, Katherine of Sienna: "I am He Who Is, you are she who is not."
Each life has its chance, to attain metanoia, a change of heart, deliverance, salvation, to burst out of the karmic bubble and ascend. Another life is not another chance, it's just another life undergoing the same trials and tribulations, all the lives all around us are undergoing, in their way, the same thing.
We no more lived in the past nor live in the future any more than we live concurrent and simultaneous existences here and now ... and yet we do.
In Atman, of course, there is no past nor future, no here nor there ...
When 'it' ascends, the residue of all those lives is burnt up, is blown away like chaff on the breeze, abandoned to hell, be it Hindu or Buddhist or Christian or whoever, like the dead in
gehenna (Christianity) or the lost souls who dwell in
samsara, in
hades (Greek) or
sheol (Judaism) or
yomi (Shinto), or wherever ... take your pick, they're all the same ...