ESO Werewolf spawn location: Reaper's March.

Does it really have to be full moon?

This is one of at least seven spawn locations in Reaper's March. Werewolves and Bloodfiends will appear at one of them, about one night a week. If they are killed, that's it till next time.
You may be better off waiting at the Rift Werewolf shrine during the day: Many players bite for free there.