Molly song in the 1960's - Cars & Trucks

In a 1960 model 'any car' , a manual transmission
remove/repair/replace should be fairly straight forward.
I couldn't find anything to help BUT, I did find an Alvis Car Club.
Maybe someone there will guide you.
http://www.alvisoc.org/t/AboutUs

Do you know how to use a search engine?
https://myclassicgarage.com/marketplace/knowledge_base/1960-chevrolet-impala#performance

http://www.automobile-catalog.com/performance/1960/295520/buick_invicta_2-door_hardtop_turbine_drive.html

By key or push button? If by push button you have a wiring problem. If by key probably lack of lubrication on mechanism. I'd try WD-40 before doing anything drastic. This may also apply to push button if the mechanism is not lubricated. If there is a click when the push button is pressed the wiring is probably ok.

You real that a person has to be 70 years old to
even have worked on one of those

You need to find a Corvair internet forum

Here is the link to your 60' caddy wiring diagram.
http://www.auto-wiring-diagram.com/wp-content/uploads/2011/08/wiring-diagrams-of-1960-cadillac-all-series-part-2-e1313734688375.jpg

just spray it a little if needed with WD-40 to help loosen then I pry it forward from behind with a good size screwdriver or similar, and it just kind of rolls out.