[ChevyGuy]

As I think you've figured out, the brake position sensor isn't a brake switch, it senses the position of the brake pedal. This is used by the computer to know what you're doing as well as being used by the BCM to act like a brake switch.

I'd look at a problem with the pedal itself. I'm thinking it's not always going back to the same position. I'm sure over time the computer looks for the "highest" position of the pedal and considers that "home". If the pedal doesn't return back to "home" then the brake lights will remain on. In other words, I don't think this is an electrical problem so much as it's a mechanical problem. The pedal must consistently return to the same exact position each time.

 

[ChevyGuy]

The positioning sensor is actually 2 sensors (for redundancy). It's two variable resistors. So the three lines (for each sensor) are power, ground and the sensed position. All of the lines connect back to the BCM which uses the information for various things - including the brake lights. The brake lights are driven directly off the BCM. No relays.

So for some reason the BCM is deciding to turn on the brake lights. My guess is that somehow the BCM is losing it's calibration. I'd assume it's because of some kind of mechanical fault that causes the sensed home position to be unstable. There are various codes that are described if the sensed value goes outside of limits - such as you'd have with a short or open. But I suppose a bad connection could cause problems without setting a code. You might want to throw a scanner on it and see if there's any codes. (Of course disconnecting the battery has cleared them. You'll have to wait for a occurrence.)

It seems to me you've already changed the part that would be the most likely suspect. Only thing I can suggest is to look at the linkage and see if there's any slop. Changing the BCM would be rather expensive, and strikes me as unlikely.

Of course, I'm assuming there's no aftermarket stuff attached anywhere that could affect this. I'm not sure what it would be. An aftermarket cruse control? Anything plugged into the OBDII connector?

 

[ChevyGuy]

An update, the brake linkage was sticking intermittently!

Cool! Did you find the cause of that?