The easiest way to install a Hi-Mount Brake light would be to splice the new light in to the trailers existing brake lights. There is no need to go back to the TV's High Mount as they are all electrically the same point and will all come on together.
The bigger issue is running the wire from the existing brake light wiring up to where ever you want to mount the new light. If you can access the existing brake wiring harness from inside your trailer that would make it a fairly easy install with all the wiring concealed. If you can't you could always run it along the bottom of the trailer and then up behind the spare tire to mount the new light. If you go that route make sure you use a wiring harness wrap, a black plastic split tubing, to protect the wires from fraying. If your rear brake / tail light are a dual filament bulb make sure you splice in to the brake light wire and not the "tail" light.
I think a High Mount 3rd Brake Light, like a Jeep Wrangler's spare tire bracket mount, would look pretty good above the trailers spare tire.
2017 Sunseeker GTS 2800 QSF
TOAD: 2016 Ford Edge Titanium FWD