When replacing the brake switch, why would only the third brake light work and not the other two
It is possible that both of the brake light bulbs are out. It is also possible that the other two brake lights are on a separate fuse from the third brake light which could cause the third brake light to work separately from the other two. I would recommend having a certified technician take a look at a wiring diagram to see the brake light circuit layout. This will help the technician to determine the cause of the brake light issue.