It could be due to a problem in the voltage regulator--when you load the supply down with something (the brake lights or turn signal), the problem goes away, but after the load is removed and the capacitors charge back up, the interference starts again.

Most quality sound systems have noise filtering on the supply as well, so you may have a problem with the either the power to the radio, the filtering to the radio or the radio itself.

It may also be a loose ground connection somewhere, too...