OK you have a small manual fridge.
The flame is not a pilot flame......that is the main flame that you light using a piezo ignitor.
The thermostat adjusts flame size depending on setting.
Max setting.....high flame ON continuously
Closer to OFF setting smaller flame size..less cooler fridge.
When temp reaches set point flame will go into bypass mode (very small flame)---on electric operation element will turn off
Operation while stationary....fridge needs to be level.
Level is close enough if you are comfortable walking around (no tilting) and laying down no blood rushing to/away from head)
While in transit....the rocking back and forth of rv will keep coolant solution in motion so it's not a concern.
HERE is a decent manual that covers the small manual fridges.