Turn signal not working when brake light comes on. 
Are they on separate bulbs? On a Bushtec (with the six wire plug) they would be. If you have the brake light and turn signal overlayed on the same wire to the same filament of the same bulb when the brake comes on it's on all the time. It's not that the turn signal is no longer blinking. There's just something else on the same circuit that is hot all the time.
Bike isn't like the car. The turn signal switch in the steering column of the cage separates all four corners of the vehicle and separates brake and turn signal for the rear. So the home-run from the turn signal switch to the rear corners have already have t/s and brake light feeds isolated before they leave the steering column.
Bike isn't that way. Separate feeds for the brake light and turn signal all the way to the back end on a Harley. Because they go to separate bulbs. Never intended to be run together.
Do you have separate bulbs for brake light and turn signal? If so you've just got the brake light feed and turn signal feed crossed somewhere.
If not you either need to mount an extra pair of lights and wire the t/s and brake lights separately or use one of the several types of accessory modules (Badlands) that will make a bike's turn signals also show brake lights. If you use the module you'll only need a four wire plug to the trailer (rt, lt, rl, grd) as you won't have a separate brake light feed.