Turning on the running lights through the trailer plug

I think I figured it out finally. I had a bad ground wire. Battery was good. I ran a new ground to the frame and everything seems to work the way it should. I'm not sure how far back the original ground wire ran or where it was supposed to tie in. I assume it goes back to the inverter box (or whatever that is actually called). I'll dig into it further when it cools down here. Thanks for everyone's suggestions.