You have to provide "proof of current location" - we had to provide our accomodation receipt, passport stamp for Vietnam, and our boarding pass (make sure you keep your boarding pass!)
Key word "hopefully". So many stories recently of people being denied entry in this scenario. Immigration is cracking down on 'tourists' who are spending too much time. Probably best to get a visa or use a fast track service.
"you just drive into Mexico and stay anywhere for anytime" Surely you can't be that naive. But because you probably are, just go ahead and do that. Thailand is doing fine without you