I'm adding a three wire ( red,blue,brown) tail/stop light to my pocket bike with some problems. The problem I am having is when I have the lights on my brake does not work,but when I turn them off the brake light works great.so what am I doing wrong please help

Brake systems require a separate ground. Otherwise, it will try and ground through the other lights and they will go out.

I would identify what each color wire does.
If no separate ground wire, may be intended to be grounded to frame.
Feel it should have more wires
Tail
Stop
Right
Left
Ground
Scratching my head with 3 wires.
Ground an apply 12 volts to the 3 wires one at a time. Good Luck