I just replaced the brake switch on my 2000 Alero; one of the switches has one connector, the other switch has two connectors. The brake switch is the one with two connectors. The other switch turns off the cruise control when you hit the brakes. Since you've had your head in there to the point where you can see the brake switch, it's easy to remove. It turns about 90 degrees, then pops out. It's easier to pop it out, then remove the connectors. Before you remove it, note how far in it's mounted. There are several rows of "fins" which allow you to adjust how close it is to the brake pedal (how soon the switch makes contact). You'll want to reinstall it in the same position. Once you remove it, you can take it apart and wipe clean the contacts, or just get a new one. AdvanceAuto had mine in stock. (~$15 ?) I cleaned mine about 6 months ago, worked for awhile, then I just replaced it.
Hope this helps.