Back up lights on when trans is in neutral

I'm real near the complication of my car. Yesterday, I installed the battery to test the electrical systems and found that when I turned the key to the on position the reverse light under the dash and the ones in the tail lamps came on. The trans was in neutral at the time. I removed the back up light switch from the trans and found that the switch is made all the time. I would assume that the switch should be open when the ball on the end is not depressed. If so then it looks like my switch is the problem. I checked Rock Auto and they do not list one for a 1969 car, but they do list ones for 1970 and later.
Dose anyone know if the 70 and up switch is the same and that it will work in the 1969 trans?