Ok, glad your tstat has arrived and is helping you out.
Ideally, yes, you want it outside the enclosure between the UTH and the glass. Where you have it no is ok, but you still may have headaches with it there. Your snake can and will move the probe. This, in turn, could cause a heat spike because the probe is no longer reading the actual hottest part resulting in inaccurate readings which in turn will kick the temps up.