The logs that businesses are keeping in NZ are quite funny. The whole ‘write something on this bit of paper’ process is basically opt in as far as I can tell.
If the place you went to doesn't have the sanitiser part then they're probably breaching their public health obligations. You can ask them to put out sanitiser or report a breach.
https://forms.police.govt.nz/forms/covid-19-breach
As an aside, I'm impressed in NZ that there's a central place to report issues but then issues are dispatched to the right agency to follow up. That makes it super easy to report issues.
[0] https://www.stuff.co.nz/national/300016238/nz-covid-tracer-w...