Change the switch. Rock Auto has the Delco switch with the side terminal for about $18.00. I did a search for a 1960 Chevy 3100 with a 235 "Starter solenoid" (not "switch") It's about halfway down the page.
It's a Delco D928A
http://www.rockauto.com/en/catalog/chevrolet,1960,c10+pickup,3.8l+235cid+l6,1489472,electrical,starter+solenoid,4188
If you're running some sort of cobbled-up home brew HEI system, good luck if you break down on a weekend in Podunk Junction USA.
Jerry