Brake Light Keeps Coming On...

I have a 1995 Toyota Avalon with 125,000 miles and the Brake Light comes on when I begin to accelerate and goes off after a few seconds. The emergency brake is not on; I've checked and check every time. Anyone have a clue as to what could be the problem? Any advice would be great. Also any recommendations on where to take it besides the dealership would be helpful.

Thanks!!!

Check the brake fluid it might be low..that is why it comes on when accel
and then go away when stable out.

Agree with 2slow2furious, your brake pads are probably getting close to renewal time.