What's the model number of the fridge? Are you sure it isn't LP/AC? In either case, even on LP, the fridge requires 12 volts DC to operate the control board and gas valve. It sounds like the fridge isn't getting 12 volts when the motor is not running. You likely have a separate house battery (separate from the battery for starting the motor). Is it in place and charged? If you bought the motorhome used, it may have come without a house battery in it. Finally, an absorption refrigerator needs to be fairly level to operate - but out of level won't cause the issue you're seeing.
Rob
U.S. Army retired
2020 Solitude 310GK-R
MORryde IS, disc brakes, solar, DP windows
(Previously in a Reflection 337RLS)
2012 F350 CC DRW Lariat 6.7
Full-time since 8/2015