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The inverter has to deliver 500 watts for this fridge. One of those plugs is for the fridge (the one that hooks up into the control board and the other should be for the ice maker. Let me get you a copy of the Norcold Service Manual for this model and that should help here. The size of the solar panel and equipment will determine how well that would work so get back to me with those specs and I can offer more.
Just checking back in to see if you were able to resolve this issue or do you still need some additional input from me here?