AustLit

Two versions of this film existed: the original silent version (1928) and a later version with an added soundtrack (1937).

Most sources state that the 1927 silent version was produced solely in Papua New Guinea, though at least one newspaper explicitly states that it was produced 'partly in Australia and partly in New Guinea' ('Australian Films', Sydney Morning Herald, 28 July 1928, p.15) and many others casually, and without context, describe it as an 'Australian film'.

The modifications for the 1937 version, however, were done in Australia:

The film 'The Unsleeping Eye,' produced in New Guinea by Mr. Alexander Macdonald, F.R.G.S., has now been made into a sound film in the Cinesound studios (Sydney). [...]

The whole production, with the exception of the leading man–Mr. David Smith, who is a London journalist was the work of Australians [...]

Miss Osborne [lead actress] stated that Captain Stevens, the well-known Sydney radio announcer, had supplied the dialogue story throughout the entire picture, but the sequences just added at the studios were all talking. Incidental music had been supplied by an Australian Broadcasting Commission orchestra. ('New Guinea Film. Now Given Sound', Cairns Post, 29 May 1937, p.6)

Some sources suggest that this film, along with its successor, The Kingdom of Twilight, and a film set in the Klondike, which was apparently never made, were designed as a trilogy:

The film to be produced in New Guinea will probably be 'The Unsleeping Eye,' and will be the first of an Empire series. The part of a story set in the Klondyke has already been photographed, and the company will produce a third picture probably in Western Queensland.

Source:

'Film Story Set in New Guinea', Kalgoorlie Miner, 1 August 1927, p.4.