Possible electrical issues in my 64 wagon
Look at the wire that goes between the starter relay and the starter solenoid, it's about a foot long 12ga brown wire if it's still factory...
I had the same issue you're having, that wire had vibrated enough over the years that most of the copper strands inside had broken. If I held the wire just right, the car would start.
I replaced it with a scrap piece of 14ga, and no issues since.