Oh I missed that part about watching someone when they hide. I recommend splitting into randomized pairs then. First player in the pair hides, the other watches the first player. This way, any pairing where a PC (possessed/cultist) is first, they get identified immediately. The cultists may try to throw us off by using stuns, so we'll randomize the pairs again but ensure no two people got the same person as before. Repeat this twice more until everyone has been observed. I believe we have 11 players right now, so it may take a couple extra rounds to verify the last person.
I know this went terribly last time, but I can randomize the pairings in chat with dice rolls. The "rules" would be to roll a 2d11. These two players (based on order of the signup list) are removed from possibilities, and a 2d9 is then rolled. 2d7 is then rolled, until only one person remains. The first person in each pairing is the hider, the second uses watch on the first person. The leftover person can randomly choose one of the second players in the list to unveil, as a deterrent to PCs that would attempt to use stun instead of watch.
Ok I think I realized a better way to do that. Instead of pairs, groups of three. One person hides, another watches the hider, another unveils the watcher. The groups are still randomized, but two groups would have 4 people I believe, so they can also unveil the first unveiler. This way, everyone's actions are accounted for. Every other round, everyone in the game unveils the person below them in the signup list, because watch can only be used every other round.