I ran a wire to the lamp, and could not get it to come on. So, I took the socket apart and find that the internal contacts were very dirty/corroded. I cleaned it up, and soldered a new wire in. Here are a few pics and a video of me testing the gravity switch....
components of the lamp...
the switch taken apart, with the spring that goes around it and the c-clip that holds it into the socket...
new wire soldered to the contact...
installing the c-clip to the base....
testing with continuity test light...
