OK, let me start off by saying I love my car…she is trying my patience though…I have a 1992 Toyota Tercel with close to 200k on it. Recently I have had to replace the alternator and a few other things…the NEW problem is that the brake lights stay on…ALL THE TIME. The brake feel the same, I heard no clunks or pops…the lights just stay on. I have to disconnect the battery when I park for a while, and its unsafe. Where do I start looking for the culprit??
A stuck brake light switch? I will let others pitch in, but usually somewhere around the upper pedal area.
Second vote for a faulty brake light switch.
I am all for it, but where the heck is it…what the heck does it look like…and how the heck to I really get down there to look? 
I have an '88 Toyota Supra. I just recently had the same problem. I immediately looked to the brake switch under the dash that is actuated by the brake pedal. What I found was remnants of a rubber disk that was used on the tab of the brake pedal to push in the brake switch plunger, and the plunger sticking through the hole that was used to secure the rubber disk! The hole was the same size as the plunger? Who designed that? My guess is the rubber disk was designed to keep things quiet, but you drill a hole the same size as the plunger? A penny and some JB Weld fixed the problem, but that situation still burns me.
Rant Over…
If you look under the dash, and move the pedal, you’ll (hopefully) see the switch move with it. Generally, the switch is atached firmly to the dash support, and the pedal will push the switch plunger in and out.