What does "up the boohai" mean in New Zealand?

"up the Puhoi" — slang far from civilisation. The Puhoi is a river just north of Auckland. Over the years the phrase has evolved and is now often heard as "Up the Boohai". It is also sometimes attributed to other New Zealand rivers. Again, more characteristic of the older generation.

https://en.wikivoyage.org/wiki/Puhoi

Ah Puhoi! I remember it well. Great pub, astounding views, good people. I also remember my Dad, when asked where he had been responding " up the Puhoi shooting Pukekoes with a long handled shovel" meaning of course 'none of your business'but basically my understanding is as beeaydee states far from civilisation, equivalent to Aussie's 'beyond the black stump' or 'back of beyond'.

'Up the boohai' means "lost."

boohai: out of the way, remote or non existent place, often in 'up the boohai' to mean lost, or 'up the boohai shooting pukakas' meaning lost, possibly in the head.

http://www.samyoung.co.nz/2019/11/up-boohai.html

I recall that my Dad sometimes used the expression "Up the Boohai" to describe poor reasoning or irrational behaviour. He was a WW I vet and he told me that the term was used by the troops to describe some of the officers' decisions, as in "These are the orders but they're all up the boohai."

The coastal ferry from Auckland used to travel up the Puhoi estuary to the small settlement. Large numbers of Pukeko birds would be disturbed and fly across the path of the ferry. Passengers would line up by the boat rails and fire their muskets at the slow flying birds.
This activity was considered great fun and well known by all.
They nicknamed Puhoi "The Bohoi" because a community of Bohemians had settled there. "Up the Bohoi shooting Pukekos"
In those days there were no mangroves in the estuary and the channel was deep enough for the ferry.