To my eye there is not a close fit with any of images for the species images shown online at the ALA page for the Technitis Group, or for Conchylis amaoenana for that matter. C.amoemana apparently has an extra white wing band and the markings at the wingtip look different.
I think this is a Gellechiod moth, probably Oecophoridae. This is based mainly on the labial palpi, that I think are just visible in one of the photos. The CNM photo of T. amoenana shows the quite different Tortricid palpi which would be expected to show on the current photo if they were there, and a different wing pattern. I've checked out a number of Oecophoridae and Xylorictidae prospects without success so far.
I was wrong about being able to see the labial palpi in one of the photos, they are obscured. The moth is Scaptesyle sp in the Arctiidae. There are several similar species (including equidistans and middletoni) that are generally more northern, but ANIC has a couple of ACT and south coast specimens. I can't match the photo exactly to any of them, but the photo seems to fall within their range of variation.
I note there are differences in forewing markings between the two sightings here on CNM of L. cataphracta. I have sought Glen C.'s opinion regarding S. undescribed species.