Update - I posted my request quoting my Singapore ticket number and flight details via the ANZ website and received the following reply;
Kia ora,

Thank you for your query regarding seating on your Air New Zealand flight.

As your booking was ticketed through Singapore Airlines, we would need to request seating on your behalf for your Air New Zealand flight.

You are able to view the seat map for your Singapore to Auckland flight here. As all the seats in Business Premier are aisle seats, please let us know if you have a preference for the left, middle or right hand side of the plane. Do note that all seating is subject to availability and business requirements.

We look forward to your reply and assisting you further.

Kind regards,

Service and Support - Email
Air New Zealand

In response to this I sent a request for seat 04A and received the following;

Kia ora Peter,

Thank you for your reply.

I have selected seat 04A for your flight from Singapore to Auckland as requested.

Please get in touch if you need assistance with anything else. Otherwise, we look forward to welcoming you on board.

Kind regards,

Service and Support - Email
Air New Zealand

All very straight forward, well done ANZ.