First, Ford often ships new trucks with the relay for the trailer charge circuit not installed. On the two I owned and more I test drove, they were in a plastic bag in the glove box or behind/under rear seat. Consult your owners manual for the location of where it goes and verify in your distribution box. For a check on that, as All I could afford said, truck running in park, check voltage at RV battery when connected to 7-pin is higher than when truck off.
Etrailer has good diagrams, vehicle side outside, RV style.
Besides that, in 2 hours you may have depleted your RV battery running the fridge off an inverter. You should do a power analysis on your RV. I too recommend using fridge on propane instead of inverter.