Your best bet is to go to the King Country, or even better, the Taranaki Blocks. Try to get to south or west of Piopio at least. I know it's a bit of a drive from Matamata, but well worth the time IMO. I've had success quite consistently in that general area.
Not too familiar with the Taumarunui blocks but could be worth a try. Last time I went that way there were countless goats by the roadside, but not a single one once I was in the block.
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