Looking for Relatives of Sullivan OR O Sullivan of Waihi Nz Miners

My father's family lived in Waihi and as far as I know worked in the mines. His father William James Sullivan or O'sullivan died in 1913 when my father was ten months old. I have not met any of the family but believe my grandfather had siblings named- Annie (lived in Hamilton??), Mary, Stephen (who had one eye), Martin, Leo and Patrick. There may have been others. My great grandfather was John Sullivan/ O'Sullivan and my great grandmother was Mary (nee Regan). There is some uncertainty as to whether the name is Sullivan or O'Sullivan - different documents give differing names. I also heard that the great grandparents possibly came to NZ from America. It would be great to know something about my dad's family.