[jeffba]

Tom you were way off. But right on for government work.
Open circuit battery voltage 12.7 volts
Current draw with inverter and "key" switch off, 0.25 Amps
Key off, inverter turned on for refrigerator 9.5 amps (doors were open so lights inside refrigerator were on)
Key on, inverter on, 13.5 amps
Measured with Clamp on meter

So I am thinking a 10 watt solar panel would be what is needed to just maintain the battery and keep what Montana thinks needs to be left on with battery disconnect switch off.