Originally Posted by Velo Mule

I don't know if you will be able to get the solid cable out of the cable housing, but if you can, grease the cable really well. Cables are hard to find an preserving yours will be important. You might even be able to use new housing on it. It has been almost 40 years since I looked at these systems. The key is to keep that cable happy. With the cable moving and the derailleur cleaned and lubed, it should work well.

Wait a second? That has a Schwinn welded on kickstand!?!!! I don't remember that. I never knew Giant made bikes had the Schwinn welded on kickstand. I learn something every day.

When it is back together we'll want pictures and a ride report.