The timer is probably narrative only. Actual timers tend to really badly ruin the fun for a broad swath of player audience and this sort of false urgency tends to be a normal thing in RPGs both Western and Japanese. That said, I just wish I could switch party make-up without going to camp every time. But I've gotten to 4th level on 3 rests and I have a friend who last I heard had gotten to 3rd on 1 rest. There doesn't need to be anymore limitation on rest...maybe have an achievement for getting to levels without resting.
