There isn't a compressor, or anything in this fridge that resembles a home unit. In other words, no moving parts except the door. It may take the fridge 24 hours to cool. Keep checking, but not too often.
As for the "auto" switch being in electric mode, are you sure you have power on the trailer.? Did you test any other plugs? Will the Microwave work?
2012 Ford F250 ext. Cab 4x4
2002 Jeep Wrangler Sahara
2008 Yamaha V-Star 650 Classic
2008 Work and Play 18LT