Maybe I missed something along the way, but the GCFI outlets are going to only work when you are hooked up to a generator or shore power. They are not going to run off of a 12volt system. Only certain items will run on 12 volt power, outlets are not one of them unless, you have an inverter installed.
It seems like the GCFI is hooked up properly and I'm not sure if it would help or not, but you can purchase a GFCI circuit tester. I have one that has 3 lights on it and then it has a legend on it which gives different combinations of the light when you plug it into the outlet. It will tell you if it's hooked up properly, missing ground, neutral, etc. It might be worth trying something like that just to make sure, plus they are pretty handy to have around the house.
Mine also has a button on it which you can press the button and trip the GFCI, I bought it because my builder wired other outlets to a GFCI in a different room and I couldn't figure out where it was tripping.
2012 Keystone Sprinter
Still sticking around for the good people and advice.