That switch is either not working (stuck closed) or miswired and something else is providing +12v to the terminal on the heater that activates LP gas mode.
I would do two tests:
(1) Disconnect the switch and check for continuity, to see if it remains closed (zero resistance) in both the On and Off positions
(2) The brown wire to the heater controls should be the LP mode. Disconnect it and see if the problem goes away. If it does, you will need to trace back and find where it goes. Also, see if that wire has +12v on it when the LP switch is off.
2004 American Tradition; 2014 Buick LaCRosse
Homebase in the Ocala Nat'l Forest near Ocala, FL