trailer marker light doesn't work

If I am following you correctly you're just having problems with the left tail light (running light, stop light and turn signal) working correctly.  If that is correct then I think the problem is in the grounding of that tail light fixture (left) only.  The ground from the trailer to the TV should be good because the right tail light is working correctly.  Hope this makes sense to you and helps.

Actually, I mis typed. Both the left brake and the left turn signaling don't work correctly. We checked all the circuits on the TV, plug and cleaned them. They are working well, and then we did get a very weak brake ond turn signal light on the trailer. We think it must be a bad wire (ground?) somewhere along the trailer. We added a bluetooth magnetic light system that we put on the back jacks for a quick temp fixand will have to have it checked by someone with better electronic expertise than we have. But we did have a 3 hour auto zone experience where 2 nice and knowledgeable folks helped us trouble shoot. Our new/used camper needs service. Thank you all for your thoughts.

Again I had the same situation where all the running lights worked and the brake lights as well.  The turn signal didn't.  My tow vehicle warning system indicated turn signal failure and you could hear the flasher was faster.  Occassionally I would see a brake light warning as well.  When I redid the 4 wire plug everything worked so I would check those connections.  When I used to wire trailers my recollection is turn signals were a seperate circuit but brake lights were running light and brake light combined so you got both when you put on brakes.  The OP said brake lights and running were working.

Okay. Thanks for the clarification. I don't have the Escape anymore, so I can't compare what I did as I don't remember whether it plugged into the factory 4-way or not.