I am grateful to Greg Kaighin and Donna for seeing through the mists. It is now established that I am directly descended, via the Thomas Kaighin Jane Caine line from Ceasar Caine and that the Wesleyian (then Anglican ) Caine was Jane's brother Caesar Thomas Caine. (He seems almost to have been as prolific a writer as was Hall Caine.) All this might explain an on-going Australian-generations' interest in literature and art generally. Who knows.
I do have another query which concerns the occupation of Caesar Caine Senior. Nowhere can I find any reference about him. Does anyone know? I would be grateful for any indication of what sort of person he was and his occupation.