what could possibly go wrong?
oh...wait you already know the answer to that question.
What you need is called an isolator relay set,
it is a set of four relays that you can buy from either Dauntless or Bushtec for around sixty bucks,
It will "isolate" the trailer wiring from the LT wiring (cheap insurance)
Most common trailers use a four wire system,
lights, brake, left, right and of course a ground,
they use the brake light filament for the turn signal.
You cannot do that with the LT, it has a separate brake light circuit (five wires)
what you need is a separate brake light on your trailer.
The cut wire inside your trailer was probably intended to be used for an interior cargo light,
since it is already there you can use it to power the brake lights that you'll need to add to your trailer,
I repeat you cannot wire the brake light into the turn signal filaments,
the 4 into five converters that you buy at Wallmart won't work.