It is apparent that the missing female child was born about 1872. Not found, so far, in the NZBDM Birth Index.
Joseph continued as a carpenter, and in 1893 was listed as one in Hunterville. He obviously travelled around a bit. John Francis was born in Invercargill, and he was long resident in Thames (probably around the gold fields). There was also a PUNCH family in Westland - around the goldfields there, but I have not yet tracked through to see if they belong.
His son John Francis was very, very successful in life as a sawmiller and picture theatre owner. At one stage he was in partnership with John Carter, whose sons created Carter Merchants, which became Carter Holt Harvey. John Francis and his family were also the first settlers in Raetihi, and he had a substantial home which still stands. Various family members who had lived elsewhere ended there lives in Raetihi and are buried there. Hunterville is not very far away, either.