I'd run an extra wire to the starter that comes into the vehicle and attach
it to a voltmeter.

Run the car till it fails.  Then look at the voltage on the meter as you try
to start.

If it stays high, then the problem is in the starter.  Just replace it.  If
it
takes a dive to 0, then the problem is before the starter, somewhere
back the wiring.

Follow the problem back with the voltmeter.  You're going to find
where it's high at one point on the 'battery side' and low on the 'starter
side'
IF the problem is in the high current circuit.  Heck, it could be the
battery terminal is dirty.  (Or the motor block ground strap)
If the problem is at the starter solenoid, before you blame it, make sure
it's getting the start signal to kick on.  I've seen Ford solenoids that
click and appear to function but just won't work.  I loosened up the
nut holding the starter cable and tightened it back down and it worked
fine.  Turned out that the 'shaft' that you bolted to could 'twist' as you
tightened the nut, and internally move to where it wouldn't make a good
contact.  I saw the same kind of thing happen with my Dodge Caravan
with the Mitsubishi starter with the built in solenoid.  I ended up taking
the cover off the solenoid portion of the starter and found a brass bar
that made contact when energized.  Moving the nuts would cause it to
shift the contact points slightly and it would work.  For a while.  Then
fail again.  The bar was pitted, so I just flipped it over to the other
side which looked smooth and virtually new and it worked until the
vehicle was 'retired' 100K miles later.  By the way, that usually
acted like a 'thermal when it was failing.

Mike

My 77 Chevy van did the same thing. Especially when stopping for gas after
pulling the boat. Tapping the starter motor while someone turned the key
started it. New starter motor and solenoid fixed for the next 10 years..