I looked at this about a year ago. Wasn't for hunting access though, was for other reasons.
Read this https://www.walkingaccess.govt.nz/kn...d-legal-roads/
It's a matter of determining which body is responsible for the ULR and talk to them. Maybe that is DOC in your case?
If you do stick with your rights and access the URL you need to be very sure that you are on the URL and not on the private adjoining property. Determining this could be difficult.
Some, (not all) farmers will deny the existence. Not sure I blame them for this given the mayhem that could occur with some types of people accessing.
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