Most times the brake light is on for the simple reason that the ABS light is on. The ABS light on an 02 s-10 9 times out of 10 one of or both of the front wheel bearings are bad jack up the front end grab the tire at 12 and 6 o clock and shake if it moves the bearing is bad. Its pretty common of s10s my cost is about 104$ yours is probably around 200$ but see if someone can read the code see what the computer says get the code and tell me what is that helps tremendously! But like i said check the wheel bearings thats my advice.