Below is the part of the my long Fall 2013 Interior Project post that addresses cleaning the seat transmissions. I will put a link to this on our Help Page.
The 6 way power seat transmission was disassembled, cleaned and new lithium grease added. The casing comes apart via Phillips screws. Be sure to note the way everything comes apart. There are not that many parts and pretty hard to put back together incorrectly due to gear orientation, but you should go slowly and note the position of the pieces.
The cavity and solenoid shafts should be completely cleaned, especially the the shafts the gears slide up and down on when the solenoid is engaged. Over time, the grease dries very hard preventing the solenoid slide plates from popping out and sliding on the shaft to engage the seat cable gears. I use 0000 steel wool and WD 40 to clean shafts and cavity. Make sure the slide plates on the shafts are slid completely off the "squared" section and all dried grease is removed.
NOTE on grease: I have had good look with white lithium grease, wheel bearing grease, synthetic grease, conventional grease... so use whatever type grease you like best. Whatever you use, will probably have specs that far exceed the greases used in 1963/64.
I had to really bear down to get the old brown dried grease out of the cavity. Here it is nice and clean:
Ready to put back together: