The honest answer
For most small and mid-sized New Zealand businesses, the first meaningful movement comes within two to four months, and the bigger gains build over six to twelve. Anyone promising page one in a fortnight is either targeting searches nobody makes or taking risks with your site.
SEO compounds. Each improvement makes the next one more effective, which is why the early months feel slow and the later ones don't.
What decides how quickly it works
Where you're starting from matters most. A site with technical problems, thin pages or no clear service pages has to be fixed before anything else can rank.
Competition is next. Ranking for a service in Taupō is a different job from ranking for the same service across Auckland. The history of your domain, your reviews and how often other sites mention you also play a part.
What you should see in the first three months
Technical issues fixed, service and location pages improved or added, and your Google Business Profile tidied up. In Google Search Console you should see more searches showing your site (impressions) before you see more clicks.
Rankings for longer, more specific searches usually move first, for example 'heat pump installer Taupō' before 'electrician'.
What you should see by six to twelve months
More of your main service searches on page one, steady growth in clicks from Google, and enquiries you can trace back to organic search. This is when SEO starts lowering what you need to spend on ads.
How to make it faster
Fix the technical basics first, give every main service its own page, answer the questions customers actually ask, and collect Google reviews consistently.
If you need enquiries while SEO builds, run Google Ads alongside it. The search terms data from ads also tells you exactly which pages to write.