Obviously I stand to be corrected, but as I understand it that is the local requirement of NZ CAA.
NZ was one of the earliest countries to embrace ETOPS and for the 767-200 half the experience operating that type on ETOPS was gained on trans Tasman ETOPS in the first decade or so.
Another thing is that APU's depending on the type will not relight above a given altitude (usually early 20Ks) so as to avoid cold soak problems the local requirement is to keep them running.