There are at least 3 distinct cemeteries in Otaki which I now categorise as 1. Rangiatea (original Anglican cemetery 2. Pukeatua Catholic cemetery and 3. Public Otaki Cemetery. Of these only Rangiatea is not searchable on-line
Hi Signal
Haven't been able to find a burial for John GORDON (d. 1897) either.
A good many Rangiatea Churchyard "records" are searchable at >
https://billiongraves.com/cemetery/Otaki-Public-Cemetery/249958but these are, (in the main), for plots with headstones.
I would think if "Otaki" is what is written on the death printout (and the Rev. McWilliam was the officiating minister), then that would refer to "Otaki (Public) Cemetery" as distinct from 'Rangiatea Cemetery".
But as I recommended earlier, I think the Otaki Historical Society would be your best source of assistance.

* Was John GORDON's place of birth recorded on the death printout ??
~ Lu