Replacing a brake light switch is a simple procedure.

1. Remove the two wire connector at the end of the switch. There are two plastic clips that are released by squeezing them with your fingers. Some connectors may have their clips broken off but this won't keep the connector from being used.
2. Remove the retaining clip from the end of the mounting stud on the brake pedal.
3. Pull the switch away from the pedal just enough for the outer nylon washer and the outer end flange of the switch to go past the mounting stud. The other side of the switch end is cutout so that you don't have to remove the master cylinder push rod from the pedal. The push rod fits inside between the two end flanges. The switch will just pull down and out.
4. Slide the new switch up and into place with the push rod between the two end flanges.
5. Push the switch toward the pedal onto the mounting stud and reinstall the outer nylon washer.
6. Reinstall the retaining clip to the hole in the end of the pedal mounting stud.
7. Reinstall the two wire connector to the switch and you are done.

If your connector's plastic clips are broken off, you can still use the connector. If you feel that the terminals in the connector don't fit tightly on the contacts of the switch, you can use a small thin knife blade or screw driver end to slightly bend the terminals inside at the closed end of the terminals to make them fit more snugly. Now you should have properly working brake lights when you push on the pedal.
Also remember that the two nylon washers that mount onto the pedal mounting stud are very important. These washers keep the switch tightly in place and operating properly. Without them, the switch is too loosely fitting on the mounting stud and won't operate properly. Often these washers are lost or missing. They can be purchased from National Parts Depot and other Mustang parts vendors.