Before going through all that:
Reach up in front of the underdash cover RIGHT beside the brake pedal & feel around rearward for the switch. It takes a limber arm! (You can pull the 3 plastic rivets & drop that panel if you want to look at it.) It sticks straight back and has a vacuum line just below a 2 wire connector, and it's sort of long. Push the brake pedal slightly with one hand & try to turn the switch clockwise to lock it into its bracket. It shouldn't take much force, so don't break it. While still holding the pedal forward, find the button of the switch that rides on the pedal arm. Pull that button FIRMLY forward until you hear at least 3 clicks, then release the pedal and listen for clicks as it auto-adjusts itself.
Your brake lights & shift interlock should work for at least a couple of pedal cycles - enough to get you out of Park & rolling home.