Trailer brake and stop lights not working at 7 round pin
 

I have a factory hitch and wiring but the brake and signals output leaving the car are not working. There is power to the running lights. Any ideas? It's a 2010 H3

Have you checked the fuses, trailer plug lighting circuits use separate fuse than the truck lights.

There is a known problem with the wiring harness going to the 7pin connector rubbing on a frame member just behind the rear bumper. Eventually it wears through causing shorts/opens in the harness. Follow your harness from the back of the connector towards where it ties into the harness for the rear lights. You can do a search on here, I believe someone previously posted pictures. My guess it that's where your problem is. That's where I found mine when I had those same symptoms.

What chooch said....

Dirty connectors comes to mind too. The truck is about 9 years old, the trailer plug gets a parade of crap sprayed at it all the time, not to mention outright dirt inside if you/prior owner have ever wheeled it.

Mine was packed with mud one time, had to hose it out, spray it with compressed air, then douse it with CRC electrical contact cleaner. I am not suggesting yours is that extreme, but they get a serious crud build up.