Ok, there is a definite pattern to it. It seems that there are two keys: the character that the room is based on is the key for the room to be unlocked, but there are at least two other characters that need to be in the group during the run for both rooms to appear. There seems to be a minimum of two character rooms for every run and until both rooms are unlocked, entered and completed, the rooms don’t refresh.
For instance, let’s say there are two rooms: Nayeli in the 5th room, Tommus in the 8th room. If both are in the party, win. But if Tommus isn’t, the Nayeli room will appear and can be cleared but the Tommus room won’t even show up during the run. Unless… there is either Saarvin or Raika are also in the group. So even without Tommus being in the party, the room will appear with either Saarvin or Raika, but if either Saarvin, Raika or Nayeli aren’t in the group and Tommus is, the room won’t appear.
At least… it’s something like that. I haven’t quite nutted it out but for anyone curious, I highly recommend switching 1 character out each time as you do multiple runs through a particular dungeon until you’ve found and cleared all character-specific locked rooms.