How long before you're considered a resident of a state?

I would guess you might be able to find some specific information on this via each state's website (and I would guarantee every state has one). Car registration requirements can vary widely. Not that, with an RV, you're likely to go to Hawaii, but it at least used to be true that people moving to Hawaii and bringing a vehicle from the mainland had something like 90 days or less to register the car in Hawaii, regardless of whether they were becoming official residents (i.e. even the military had to).