Since the brake mechanism is entirely mechanical it cannot be anything to do with that (can it? Famous last words!
)
But presuming your brake light works, this light will be on as long as you are pressing the brake pedal. Now normally a light coming on would not cause any interference except possibly a slight 'click' when the lighting circuit is made, and when you stop braking and the circuit is opened.
Since the interference continues as long as the circuit is made, it suggests there is some electric field coming from the brake light circuit, and the obvious place to look first I would think is in the switch which I imagine is located on the pedal box, not too far from the radio.
Another source could be the brake lights themselves, but these are some distance from the radio, plus there will be screening provided by the metal body of the car itself - even so, might be worth checking for rusty or corroded contacts or poor earthing of the bulbs and lights.
But my first bet would be the switch contacts - may be arcing, may be corroded, may be sticking and not separating cleanly etc.
An easy test will be to turn on the radio, then take a flying lead direct from the battery positive terminal to the feed to the brake lights, thereby by-passing the brake light switch. If there is no interference on the radio, this points to the brake light switch as the culprit.
