Ok, then I would say it's the ignition then. Sounds like it's crossing over a bit into start when it's in run. Replace that and you should be good. When in run, there's not enough power getting crossed over to start it, so the selonoid is engageing, but the starter is not getting power. Haven't heard of that before, but I don't doubt you at all.

 

Now you need to set a timing light on the rear cylinder(s) so you can hold the gun trigger and see if you have spark. It should run with spark, fuel and compression.

You are missing one of the 3 if it does not start is which one?

 

fuel pump or fuel pump relay possibly. cranks but won't run sometimes. Sounds like fuel problem.

 

The starter motor on these cars get hot because of their location. If you have a lot of miles on the car it might have been caused by all of that heat. Sounds stupid I know but I had the same problem. Replaced the starter and added a little heat shield. Good to go.

 

This is what I was thinking.

And I'm not sure how heat's involved except as an added wear thing, because the car's been cold (<40* soak) when it happens. And I know it's not a battery issue, because it started once after about 2 minutes of unsuccessful trying just before.