After you try the resistive load test (including hot water heater 120V resistive loads, if equipped), try this;
12V/120V fridge will normally auto-select 120V when it see both power sources available. With inverter off and shore power disconnected but 12V system on, try opening fridge door and see if fridge light comes on. If so (assuming bulb is good) you know your fridge sees your 12V. Turn 120V breaker off for fridge on the 120V side of your breaker panel. Turn on inverter. Confirm the bulb is still on in the fridge. Check current draw now that fridge is running off 12V intsead of 120V - See how the current draw is now through inverter. Good chance the fridge draws more load at 120V since it assumes it has shore power / generator supply. Good chance fridge is more 'electrically economic' on 12V since it assumes it's running off batteries / alternator.
From Nova Kool Troubleshooting guide - AC will always take precedence over 12V DC is both are available and the AC/DC module is fitted. Look at the DC fuse size - 15A fuse for 12V DC - that's 180 Watts load before it blows the fuse. At 120V it's 4 amps - that's 480 Watts load before it blows the fuse.
I see in the trouble shooting guide that the interior light is a 12V light, so you may not be able to use that being on/off as your troubleshooting component as I mentioned before. May need to use the compressor noise or an ammeter to see the unit cycle.
PASTE;
2. Electrical: When fitted with the optional AC/DC module, both AC & DC power can be connected to the module at the same time. The unit will always run on AC when AC is available. Should the AC be disconnected there is a 1 minute time delay before the unit continues running on DC. If AC power is reestablished there is no delay, and the unit will immediately resume running on AC. 2. Electrical: (cont’d) The DC models are 12 & 24 VDC (the only consideration is the models supplied with an interior light, either 12VDC OR 24 VDC). The AC/DC models work on both 12 & 24 VDC as well as from 100-240 VAC 50/60hz. (The interior light on the AC/DC models is always 12vdc regardless of the DC supply voltage). Both modules “auto” sense the supply voltages so no wiring adjustments are necessary other than following the guidelines for DC fuse sizing; DC breaker & fuse sizing 20-amp breaker (main switch) for both 12 & 24VDC applications 15 Amp fuse for 12VDC 7.5 Amp fuse for 24VDC AC (optional) breaker and fuse sizing (100-240VAC 50/60 Hz) 6 Amp breaker (main switch) 4 Amp fuse (included with unit)