the bcm powers down after 10 minutes just like rap does for the radio, might be less than 10 minutes I haven't timed it I just tried it to see if my alarm would go off by pressing the brake pedalPerhaps your right, I have never tried the brake pedal right after turning off the key.
I just know that if you get in the vehicle, after it has been sitting for a while and depress the brake pedal the lights won't come on without the key on.