I was under the dash of my 63 Dynamic and noticed a wire with a connector and I couldn't see anywhere it was supposed to connect with. The wire is orange with a black stripe, and is located under the instrument panel.

 

Map light on dash?
Steve

 

Glovebox or under dash courtesy lights if they are not installed from factory? Check with a test light for power, glovebox I believe only is live with headlight switch on.

 

Is there a wiring diagram located in the 1963 Service Manual?

 

I worked on these cars at my first job and I recall that the wire with those colors went to the power seat motor.

Memory can be imperfect, and YRMV.