Question. Does the problem happen:

a) Only when the car is actually moving and you press on the brakes and the car is actually slowing down.

b) Even when the car is parked, when the brake pedal is pressed.

If (a) then it's a loose wire or connection somewhere that's affected by the G-loading from the braking manuever. If (b) then it's likely something to do with the wiring related to the lights, for instance, something like the headlight-sense wire from your car connected to the wrong wire on the empeg. Or perhaps a wire tangled up in the mechanism of the brake pedal assembly that's getting tugged, squished, or grounded.

Or maybe the wire running to the player is just too thin and you need to run a proper one instead of using the thin one from the car's harness.