Before NZTA's recent changes, the restricted driver's license test could be taken in Otautau. However, the test is now 45 mins long and more skills are required to pass. The test is now to be taken in Invercargill. It is also no longer done in Winton.
There is nothing official on the NZTA website yet but if you have questions, contact the AA office on Gala Street, Inv.