For what it's worth, my '65 Impala used to do the exact same thing. Rear tail lights, brake lights, and dash lights would all go out in unison. Turned out to be nothing more than dirty contacts on the old mechanical switch. As already mentioned by someone else, I strongly suspect your only problem is a bad switch, not the BCM. Seems to defy common sense that a switch going from NC to permanently open or vice versa could fry a BCM. I would insist that the dealer replace the switch first and then your BCM if unsuccessful. If the BCM is already swapped, insist that the dealer put your old one back in when the new switch is installed. If everything works, then the dealer owns the replacement BCM and your only repair bill should be for replacing the switch, especially considering the BCM cost. Are they using diagnostic codes to try to fix your problem? I hope not. A diagnostic code is nothing more than an aid for finding the problem. A dealer would have to be lazy or incompetent to think that any diagnostic code pinpoints the exact problem, in this case your BCM. To the contrary, the code is just an arrow pointing in the general direction of the problem in order to give repair personnel a better idea of where to look. Obviously, the better the repair personnel, then the more they use their knowledge and common sense to find the problem and fix it correctly the first time at reasonable cost to you. Don't let them willy nilly swap out components until they find the problem, since that would harken back to the days before diagnostic systems and be an expensive (and unacceptable) repair methodology for a modern car.
Good luck!