Brake light switch, chek engine light on.

What is your question?

My brake light warning light is coming on after hitting the brakes. I replaced the brake light switch completely, but it still comes on indicating something wrong with the rear lights. All the light bulbs are replaced, everything is working but still the brake warning light comes on and will not go out. Secondly, my check engine light is on intermediate. Most of the time it's on, occasionally it is off for about 2 day's then comes back on. My car is a OBD 1 so I tested the codes and code 71 comes up, meaning the EGR system, however, it just passed smog? so the EGR valve is working. Now, there are 2 wires connected to the EGR valve with a electrical connector, I was told that that is a oxygen sensor, could that be the problem, because I did cleaned out the EGR valve from all the carbon buildup. What could it be?