Just a thought. Bad starter relay? Solenoid on Fender apron

  

I thought the same thing, so I did a test to make sure it's getting proper power through and all seems to be good there.
I'm going to check my grounding this weekend and make sure everything has a good ground.  If that's not it, I'm not sure what to do next.  

1964 Ford F100 w/ 292 Y-block
-Central Florida-