http://ouraucklandstuff.freeservers.com/AuckDeathsF.htm has is this entry: -
FITZPATRICK Died 4th May 1887 at Pakuranga, Patrick Fitzpatrick, of senile decay, aged 80 years. Born Ireland, son of Laurence Fitzpatrick, farmer, and Catherine Troy, in New Zealand 40 years. Married at Lolmoy, County Kilkenny to Ann Haydn. Buried Howick Catholic Cemetery. Male issue living at time of death - aged 40, 34, 30, 23, 20. Female issue living - aged 37, 30, 28. RG 1887/414
Informant - Emily Gill, daughter of deceased. -
This MIGHT be the same person as : -
https://billiongraves.com/grave/Patrick-FitzPatrick/17886711#
though their ranks are different, perhaps explained by being in two different regiments at different times., The holes in the top seem too small for flower holders; rather they MAY once have supported a headstone. But it is nowhere to be found.