If the NGOs have waiting lists, you can also see a Health Improvement Practitioner. They are part of a new initiative that has been set up in some GP clinics. They can provide brief Mental Health interventions and should be able to tell you what services you can access in the community. https://www.apollomedical.co.nz/news.php?ln=HIPs&LID=970314740

Supposedly, here is a list of the practices that provide this service- though it's a bit outdated. https://www.aklwellbeingcollab.co.nz/practices-involved.html

You can either ring up the GP clinics involved and book an appointment, or walk in during certain hours.