A John J PUNCH captained the City of New York into Auckland 19 May 1877.
There was a Patrick PUNCH in Hokitika, Westland, N.Z., a miner according to the 1893 Electoral Roll. He died 1904 aged 66 - so born around 1838.
Other old names I have spotted:
John PUNCH (about 1831-1885; Ross, Westland).
Walter PUNCH (1851-1934 Auckland). Walter was a carpenter who lived in Auckland from at least 1893 (Electoral Roll). Wife was Jane Barbara. He and Jane arrived Auckland on "Golden City" from Gravesend with Harriet J., Henry W., John W. - Walter and Jane are buried together at O'Neill's Point Cemetery, Takapuna, Auckland. Have found no further trace of any of their children.