clicking brakes, flashing lights

I just bought this 1997 Grand Am. When going over 20mph and applying breaks, there is a clicking noise under the dash, sometimes felt in the brake pedal. All the lights on the car (headlights, dash lights, clock, etc.) dim in unison with the clicking. Someone had suggested that the wrong bulbs were installed in the brake lights but I have checked that. Any help would be greatly appreciated. I bought this car for my teenager to drive. I can't let her drive with her lights blinking every time she stops.

sounds like your anti-lock brake system is applying itself when its not needed for some reason. have somebody check out the anti-lock sensors

most guage anomalies in Grand Ams are caused by a faulty BCM, they are located in the pass side kick-panel, and fail due to exposure to water/salt as the car gets older. Is there a pulse in the brake pedal, like the pedal pushing back against your foot? that would indicate an over-sensitive abs system. If it's just the click being felt in the pedal, I would suspect the BCM.