You're going to have a problem Dan. On a four wire harness the brake light and turn signal occupy the same wire and bulb filament. On Harley they are separate and don't occupy the same wire run. Thus the extra wires.
Cars have RT, LT, Tail light and ground. They get by with four wires because the brake light feed comes down the same line as the turn signal and then just keeps that bulb on all the time until the pedal is released. The way a Harley is wired you just can't accomplish that over four wires. On the Harley need brake, tail, rt, lt, and ground. The sixth wire is then unused or used as a power source for a cabin light or whatever other use you might have (USB charger).
Does the trailer have only dual filament bulb on each side in the rear? If so you'll need more parts. If it does have two separate bulbs on each side in the rear (likely one single filament and one dual filament) you're solution is likely to just pull more wire and make the trailer's wiring match the bike.
If it's just got a single bulb on each side in the back end you can make it work. You'll have to buy more parts though. I've used the Badlands module that mixes turn signals and tail lights to accomplish what you're wanting to do. You'll wire in the module downstream of everything else in the bike so that it just alters the trailer.
Don, actually most cars/trucks today have LT, RT and a separate brake light wire.
I bought the Hopkins converter that allows the 3 separate LT, RT, Brake to be converted into the LT, RT with both of them flashing during an applied brake pedal.
So in my mind, it should have worked. But the Hopkins guy said it would be a slight chance if it worked for me.
In the converter there has to be some diodes that keep the brake signal from back feeding into the opposite turn signal.
The weird thing is that if I apply 12v to either the green (RT) or yellow (LT) on the conveyor, I get zip out the other side to the trailer wiring. If I apply 12v to the red brake wire, I "should" get power to both the yellow and green wires, which would be the same as a normal 4 wire w/ground in a NON turn signal brake application.
Hopkins also makes a power converter that does the same thing as the Bushtec power isolator. It uses the bike leads as a signal only, no load. It has a power lead from the battery that feeds the trailer wires independently through their own fuse. So the Hopkins power converter does the same thing, plus it is supposed to combine the 3 turn and brake wires into the two turn wires.
I know there's a way to get to where I need to go, but.....