Whenever I put the car in drive, reverse, or any gear the brake light comes on. When it's in park or neutral, then it goes off. When I engage the hand brake in park the light comes on. I checked the brake fluid and it seemed fine. This is a 96 accord sedan without abs. Thanks in advance for any advice.

 

It's a long shot but possible you may have an issue with the ebrake release handle switch which operates the warning lamp. It may not be relaxing to it's lowest (released) position and it's just at that point of turning the lamp on/off. You may need to have the cables for the rear ebrakes adjusted. At least have it looked at.

P