Okay, wait. Key to Position II (RUN), the brake lights are always on, key to Position I (ON) and the brake lights are off until you press the brake pedal?

This is important...
Are the brake lights on, or the running lights? Lights are on when the light switch is on, the Brake Lights only work when the brake pedal is depressed. Are you confusing normal lights and brake lights? Brake lights should not operate with the key in any position except Position II (RUN), and when the brake pedal is also depressed.

Brake lights and running lights all go through the Lighting Control Module (LCM), so you could be having trouble with the LCM. There was a complaint a few months back on the E46 boards where the switch on the brake pedal was a problem. It's operation is not what one would expect, and as I recall there was a fuse that had failed, without the brake light fuse the brake lights are always on. The confusion comes from the wiring that passes through the LCM. Normally a bad fuse keeps lights off, not on.