I have no direct link only a family story that i cannot support. This states that in our history there is a direct link to the Christian name on the island. The way my father told it. it was the Christian of the Bounty family line. I cannot get back past my great grandfather. However the name William comes into the family and as you can see Philip Callister would have been about the correct age to be the son of the William that you are looking for. I have details on sibling of William Robert Callister: Birth.26 May 1871.

My Father: Eric Philip Callister
His Father: William Robert Callister: Birth.26 May 1871, Married.Cathrine Maria Cowell Dec 16 1908. This was his 2nd marriage.
His Father: Philip Callister: Married. Ann Wade 1855 in Kirk German IOM