For fairness, rather than allowing the same people to do night watch every single night, the schedule evolved the longer they were forced to stay in the camp they were establishing.
Rather than having one team guarding at night and one team during the day, one team would guard half the night and then wake the others up to guard, where they would then work until late morning where the others would wake up and they would have a bit of interaction for the rest of the day. The second night shift would then go to sleep early, and those who would take the first shift would remain awake and attend to the camp.
It allowed for more interaction during the day rather than behaving like ships quietly passing one another in the fog of night without much more than that. Everyone seemed happier because of this arrangement.
The monsters were kind enough to allow them to establish this schedule. Even though there were a few monster sightings from afar, none dared to come to where their camp was.