I cleaned below the awning track with denatured alcohol, and began applying the LED strip:
Here is the end, where you can see how the longer cable is attached to the strip and covered in heat shrink:
It attached easily, and seemed to be very secure.
The most difficult part was getting the cable inside the trailer. Neither end terminated where there was a cabinet inside, so I couldn't just drill a hole and run it through. I ended up running the cable to the roof, and into the refrigerator vent, and then down into the cabinet behind the microwave. I covered the cable on the roof with Eternabond to both hide and secure it.
Once I got the cable into the trailer, through the vent, I wired up and mounted the small RF receiver and controller.
I added a main switch to the power wire of the LED controller to prevent accidental activation while traveling.
The lights look great! And, the controller and all wiring is hidden.