Please be specific about brake lights: those are the lights that come on when you press the brake pedal. If that signal only works when the headlamps are on, you'll get doubled brightness. The two signals are entirely disconnected from each other, which is why you have a double-filament bulb. It's possible that the filaments are crossed/touching, and the brake light filament shorts out to the headlight side.
http://clubs.hemmings.com/baymustang/platesmall.jpgLet me check your shorts! My multimeter is just a-waiting! Formerly known as Midlife in the old VMF.
King of the Old Farts *struts*