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Did the vehicle shut down when the brake is pressed and the brake switch is unplugged?
There is a fuse for the brake lamp but that shouldn't cause a stalling concern. Do you have a way to see if any codes are present?
If you unplug the brake switch and it still stalls I don't think it's the brake switch. I would plug off the vacuum line going to the brake booster and see if it still stalls. It almost sounds like your vacuum booster is leaking and causing a vacuum leak.