I believe it's a Ruru. We had the same noise for over a year and couldn't figure it out. Then, a friend sent us this link https://nzbirdsonline.org.nz/species/mo ... ird-sounds
If you listen to the one that has the Westland petrels prominent, is it the bird you are hearing? It's definitely our mystery bird and I'm really grateful to finally have an answer.
General birdwatching discussion, help with bird identification, and all other things relating to wild birds and birding in NZ that don't fit in one of the other forums.