Since Busdaddy has seen it happen more than once, he will no doubt go with me on Monday to tell the mechanic what he has observed.
Both men are race car drivers, and they know how to communicate. I get stressed and I stutter and end up not making any sense whatsoever, so I’m always happy to have some “back-up!”
OK...
Here's my take. Of course the electrical stuff (ign switch, battery, connections, wires, and all that should be verified as functioning. But.. I'm willing to bet starter. Here's why. As the starter is used over its lifetime and the brushes wear, several things happen. Depending on the design of the starter and it's orientation, the carbon shed by the brushes as they wear builds up in the vicinity of the brush holder (no relation to Eric) and even sometimes, if there is an oil leakage issue as from a rear seal, collects oil.
Either way you end up with a mass of carbon or carbon-oil gook that eventually causes the brush to lose contact with the commutator. When this happens no current will flow.
Since in most cases, the 'ground' side of the solenoid coil is actually the 'hot' brush on the starter (trust me on this), the operation of the solenoid is also dependent on the brushes making contact. One of the signs of pending starter failure is intermittent starting, typically but not always heat related.
If you are spry enough and the starter is in a location that you can try this, carry a hammer - not a 10 pound sledge, just something massive enough to jar things you hit with it (even a big screwdriver handle will do). If and when the beast decides to balk, take the flogging device and bang on the frame of the starter. If it is the brush scenario, this will typically jar the brushes enough to allow the starter to operate (and it will work for quite a few times giving you a chance to arrange for a replacement.)
Of course, as the condition continues, instances of failure will begin to occur more frequently until even flogging it with that 10 pound sledge won't work..
But - if it quits and you bang it with the flogging device and it starts, you're definitely looking at replacing the starter..