That light is supposed to come on with the handbrake as a bulb test. As your pads wear down once they get to a thickness where you should replace them the light will come on intermittently while you brake. After a few more miles it will be on more or less permanently.
To be honest, ignore it, check your brakes visually (you already have I know). I always think the brakes are the single most important item on any car and relying on a warning light is nuts.