When waking up our fridge to propane gas, it takes numerous attempts for the air in the line to be pushed through. It helps to light the stove to flush air out from the main line, but from the junction to the fridge, the air inside must get pushed through via numerous fridge ignition attempts. It can take a 1/2 hour or longer before the fridge becomes operational on gas. Once it's working, it is happy all trip long whether you stay on gas or toggle between 110v and gas.
As stated by others, you do need to have the 12v power system operational. If the light inside the fridge is out, all bets are off.