It appears that the search comes to an end. As Greg Kaighin, Donna Douglas and Len Fargher, and others have confirmed my mother's Caine/Kaighin descent is clear. (Incidentally, of interest to Len Fargher, I had two lots of Fargher neighbours ( related ) living at Canterbury and Balwyn, suburbs in Melbourne, Australia, also born in the late 1920's. I didn't know then we had Manx connections.)

As to the Reverend Caesar Caine, assiduous searchings, even to antiquarian booksellers, ( and even obituaries ) leads to nowhere. No one seems to know when he was born, where he was educated or when he died. But he was a writer of some eminence, confirmed by the fact that his books were published (presumably by hard-nosed publishers ) and that the substance of those books reveal the acute and astute mind of no mean historian, and also, that his writings reveal a person of sensitivity and developed sensibilities almost of the calibre of a Hall Caine, (but with a greater discipline perhaps in not letting magic murk the waters of fact. ) But there seems to be a persistent, rather than a wayward gene, connecting the separate lines of Caine/Cain in that both were touched by the muse of language; or perhaps, this is a common trait in the odd Celtic/Norse swirling in this particular gene pool. But, as history suggests, who knows what really goes on in the warm hay-stacks of memory when the hormones are running as wildly and as blindly as the urgent herrings, when the time is upon them. Who knows who really IS related to whom.
So thank you all who have contributed to my search. It all ends here. Perhaps, as Greg Kaighin suggests (in jest I suspect) that no such person existed, as the Reverend Caesar Caine—a name conjured up to conceal another mysterious identity. At least that is an intriguing possibility, isn't it? And I have made some friends.
So what is left to say? Show me the gravestone of the Reverend Caesar.