Yup, back in the day, a failed solenoid on a GM starter was not uncommon, and they are replaceable.
They were pretty chap back then, but we'd pull the starter to do that anyway.
Also damaged wiring, loose cable, etc.
If it's the original starter & solenoid, 54 years is a good long run.
But it's just as likely to be in the wiring to the solenoid.