Before doing anything, is the brake system properly bled? Is the light on all the time or only when the brakes are applied? Assuming the light is on all the time, the parking brake is either applied or the park brake switch has failed. If the light comes on as the brakes are applied, there is a pressure differential between the front and rear brakes. Usually this is caused by either a leak or a serious mis-adjustment issue. After eliminating the park brake as a potential source of the brake light, Put the car in park and apply the brakes, does the brake pedal sink as the brakes are held on? This can be an indicator of an internal leak in the master cylinder which could be causing the pressure differential. Pull the top off the master, are both chambers filled equally? If both chambers are not the same, you have a hidden leak someplace. Pull all four wheels and drums, check for a broken or disengaged brake adjuster or cable. A leaking wheel cylinder will have fluid residue inside of the end caps and if the leak is bad enough to trip the pressure switch, usually at least one wheel will have wet brake linings. If this car has disc brakes, check the seal around the caliper piston for brake fluid, if one is leaking, rebuild both calipers. Finally check all hoses and brake lines for wet spots, brake hoses crack and steel lines rust out. Check these things and report back.
Dave