Not much is known about the short 1984 festival tour to Australia & New Zealand and no recordings have surfaced yet...
Although there are numerous eyewitness accounts of the Narara show, all the comments pretty much say "I was wasted" or some variation of that, although one commenter said the show was "like Stop Making Sense".
The best info comes from two concert reviews; one from Melbourne and one from Sweetwaters North. At both shows, TH followed The Pretenders onto the stage and played one long set, with the NZ reviewer stating the gig was a “two hour plus set”. Songs mentioned for NZ were; Psycho Killer, Slippery People (at which point the full band was assembled, so presumably the opening of the show imitated the USA tour), Once in a Lifetime, I Zimbra, Take Me to the River, and an encore of Life During Wartime.
The NZ reviewer goes on to mention that Genius of Love was played after the TH encore. This may be a reference to Tina’s later comment that David left the stage early, thus the remainder of the band may have kicked in an extra song or two to make-up for the shortfall.
In a comment that presages the end of TH's touring days, the Melbourne review ends with this comment: "This was Talking Heads' night. Afterwards, David Byrne was apparently heard to complain about the low standard of the performance. It's hard to imagine what this band is like on a good night."