I believe I have reached the definitive conclusion about John/Owen Thomas. His mother was Ann Thomas, second child and eldest daughter of Robert and Anne Thomas. Ann gave birth to a child on 22 September 1871 named him John but did not register him until November of that year.
Early in 1872 he became part of her parents' household and was renamed Owen for one of two reasons (a) Robert and Annie's eldest child was named John and (b) they had lost a young child in the mid-1860's whose name was Owen and they renamed John in his memory. The name of the child's father is unknown but oral evidence states that he was originally from Aberystwyth and stayed in Yns Mon for some years. Throughout his upbringing Owen believed his mother was his aunt Ann. There is a reference that Owen was Robert and Anne's grandson.
Owen moved to Liverpool in the 1890's and married Thirza Jane Pearce in 1896. He had seven children, one of whom was my father Henry Thomas.
This raises a problem for other people who believe Owen was their grandfather. There is no evidence to suggest that Owen fathered a child outside his marriage to Thirza. Therefore, anyone who believes he was their grandfather is mistaken. My own conclusion is that the Owen referred to is another member of the Thomas family (possibly a cousin). This will require further research into the history of Robert and Anne's family.
I have also concluded that Ann never married. In the culture of the time it would not have been acceptable to expect a non-family member to take responsibility for another man's child, especially as this may have revealed who the child's real father was. In addition, there was a culture of shame attached to illegitimacy at the time.
My intention is to visit Yns Mon this year to carry out further research.