There exists an almost unknown contemporaneous account from the 18th century, made by James Morrison, boatswain’s mate aboard the famous or infamous ‚Bounty‘, who made mention of a mysterious bird [… and how I love mysterious birds …!].:
“… the mountains produce birds of different kinds unknown to us, among which are a large bird nearly the size of a goose, which is good food; they are never observed near the sea nor in the low lands.” 
So, usually called the Tahiti Goose, Tahitian Goose, or Tahitian Mountain Goose – what are we talking about here actually?
We very probably do not talk about a goose, but why?
First we have to take into account who made the report:
A boatswain’s mate from the 18th century very likely was not a zoologist, but may in fact have known at least several European birds, especially poultry, so very likely knew chickens, doves, ducks, and geese, and very likely also quails, partridges and other so called game birds.
As a seafarer he perhaps may have had some good knowledge about seabirds, and probably could very well tell several species of them apart from each other.
These are the birds that we can just sort out, but what may it have been then?
Well, the Tahitian Mountain ‚Goose‘ apparently was a somewhat large, terrestrial bird, more or less the size of a feral goose, it was ‚good food‘ so it must have been easy to catch, it probably [actually very likely to almost certainly] was flightless, and it was unlike any bird known to ‚us‘, to the sailors of the ‚Bounty‘.
In my opinion, and in that of many others, the Tahitian Mountain ‚Goose‘ almost certainly was a kind of rail, a large, flightless rail, maybe a species from the widespread genus Porphyrio, somewhat like a Tahitian version of the New Zealand Takahe (Porphyrio mantelli (Owen)).
However, there is of course the chance that the Tahitian Mountain ‚Goose‘ was something completey different, we probably will never know for sure.
… mysterious ….
 J. M. Derscheid: An unknown species – the Tahitian Goose. Ibis 81: 756-760. 1939