It can only be 1 of about 4 things
1. The power wire for the break away switch is wired to a hot or turn signal wire. It should go from + on kit battery to pull switch, then to trailer brake wire. If you have a charger type one, make sure the other + wire doesn't go to trailer light or signal wire. It should go to the 12V prong on the trailer plug.
2. The brake light/brakes wire is tapped into the turn signal wire. Turn signal wires should run from the trailer plug to only the turn signal lights!
3. A bad ground wire somewhere. Grounds cause all kinds of mysterious things. You should have (1) common good ground on the trailer. See below.
4. One of the plugs are wired wrong. Here are some diagrams to go by. Use a read out type tester, don't use a light tester when checking. http://www.offroaders.com/tech/trailer_wiring-diagram.htm
Make sure you run a good ground wire from the trailer to the plug ground prong and then a ground wire from the truck plug ground prong to the truck frame. This will ensure a good ground. Letting the trailer ground to the truck ball is not a good way to do it. Plus it will keep lights, turn signals, etc from flickering or being weak.