Just some FYI, NAPA has the stop light switch, it's a common one used on many vehicles. NAPA Part number SL-134 and you'll pay much less at NAPA than other sources. They usually have it in stock too. Regarding that third wire, you'd have to trace it and see where it goes as it was not that way originally. Remember the car is almost 60 years old and things were likely changed on it. You can't assume things are original. It may be for a signal light hook up because they were optional or after-market on the J. A picture or a trace would help.
Regarding the tail lights - the ground is provided through the chrome tail light body through the tail light body mounting bolts. Because they're above and behind the rear wheels, rain, slush etc. slops up on them and they corrode big time and loose their connection. I've had to remove the four screw holding the tail light body, then clean the speednuts so they make a good ground contact. That usually fixes them. A good way to troubleshoot this take a wire and touch the tail light body and then touch the other end of the wire to a good known ground (the trunk latch catch usually works well for this) and see if the light comes on. If it does, you've got a bad ground from the tail light body to the car body. This is pretty common on the later Js.
