The older refrigerators did NOT use any electricity when on propane. They used a standing pilot light for ignition, thus no power needed.
OP, when you say the flame is "ON" all the time, that would be the pilot light is on all the time. When the thermostat calls for more "cold", then another flame lights up from the pilot light, providing the "cool"
So, yes, the flame does run all the time, but only the pilot flame. It will run for months, if not years, with just the pilot light on. Pilot uses almost NO propane.
The main burner will only be on part of the time, depending on ambient temps. With cooler weather coming, I would estimate 1/4 to 1/3 time it might be on.
