OK! Thanks for the advice all. I looked under there, and on the brake pedal bar is a yellowish rubber penis/needle (couldn't think of another way to describe it) looking thing, that keeps the brake switch pushed in when not being used.
When the brake pedal is used, the button is released, and the lights come on. It's a very small piece too, about the size of the tip of my finger (no jokes...)
Any clue where or if you can get a replacement part (if anyone has done it before), or I might just try and make a makeshift device. Or hell, even just the name of the thing - the Brake Pedal Button Penis Needle...