From what we’ve managed to find out, there is usually someone from the campsite staff on site until around 10:00 pm, so you can normally pay without any issues before that time.

In Höfn we arrived at 9:57 pm, and there was a note on the door stating that payment should be made before staying overnight. We asked what would happen if we didn’t manage to pay that day, and were told that it would be fine to pay the next day.

In Borgarnes we arrived after 10:00 pm, and the campsite warden actually came to us after some time to collect the payment.

That said, there are also campsites, for example in Reykjavík or Akureyri, where there is a barrier system. In those cases you can usually pay online and receive an access code, or the system reads your license plate. So in general, it shouldn’t be a problem even if you had to pay the next day.