The quest advances and triggers events with time, but incredibly slowly. I've tested it by having it running in the background while doing something else. (I assume time skip by resting was intended given the presence of a sleeping bag, but is missing from the caravan environment.)
When I tried it I thought it was completely broken, so I used the Unstuck feature and continued playing. I'd gotten near the end of the game by the time events started automatically playing out, and it automatically teleported me all the way back to the south end of the map. Timed events play out no matter where you physically are, it's wild.