Don't know the details of thermostat, AC etc but make sure the thermostat is in Auto mode. This question has been brought up many times and usually pertained to a Dometic thermostat. As far as I know the AC won't run on 12V at all. I may be wrong but that may be the reason it did not come on when you disconnected shore power.
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2013 Ford F-350 SD Diesel, 4X4, Crew Cab, Lariat
Sabre 2014 32RCTS, Pullrite Superglide 2900 18K
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