Chevy S10 Xtreme 2000

The brake light only illuminates and glows for either low brake fluid level (check brake master cylinder resevoir level) or the handbrake is engaged or partially engaged.
There is a float in the brake master cylinder. Bring the level to bottom of the fill cap threads. If light continues to glow try giving the master cylinder a couple of hits with your fist sometimes the float unit will get stuck down inside the master cylinder resevoir. if light is still on check the handbrake and make sure that the pedal is all the way up. Give it a tug with your hand in the up direction while holding the brake release lever. Sometimes the mechanism can stick and does not allow the brake to come up all the way.If it was stuck down some lubricating sprayed into it will work to make it operate. Rusty and sticking handbrake cables can cause the handbrake not to return fully up also.