Built in Propane Heater thermostat not functioning

I wonder if the bulb was mounted inside the heater about 1/4 the way up, close to the front grille...

I'd bet it was. It makes no sense to have an operating part of the furnace outside the grill.

Did I miss a picture of the valve/thermostat combination?

FWIW, I use a propane heater in my rig (Sportsman brand) that only has the White pilot/burner regulator valve and a mechanical ball valve. Heat is set by opening the mechanical valve for more gas delivery. I don't know if yours is similar.