Imminent failure?

I believe if the starter is spinning then the solenoid is moving to make contact to spin the starter, so there must be an engagement problem, maybe the flywheel ring gear is really worn or the solenoid drive gear/shaft is faulty.

 

Are you sure adequate current is getting to the solemoid?
Check all battery, starter and signal electrical connections first as those are prone to corrosion.
Also, Behind the Neiman mechanical key is an electrical wiper contact to carry quite a bit of current when you rotate that ignition key to "ON". Over 40+ years dust can get in there and cause poor connections or resistance. Get upside down and inspect it or shove a digital camera there to get an image. I can't find a good pic quick but here is Corbani's electrical diagram of the contacts.
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Check the battery / terminals etc first as synchro suggests together with connections etc.

If the starter engages then the solenoid is doing it job although it could be lacking amps. Could be a loose starter motor i.e bolts have come loose but that would jam up.

More than likely to be worn end spigot / bearing on the starter itself. This is a common problem.

Take it to a specialist to repair, especially if it doesn't work out. Pulling the starter isn't an easy job and you will only want to do it once.

Alternative, ditch the starter as its a pile of crap, buy a GR starter.....sooo much better

Tony

 

Funny Story at Monterey Historics for Ferrari in 1994. We had carte blanche green passes at Laguna Seca and I drove the Dino on the driving roads to that high point at the campgrounds to get some panoramic photos. Dino 05702 had been having progressively harder starting all week and culminated here in not starting for 30 mins at this remote campsite.

The final image of that weekend was the departure day, Sunday, where I had to be push started by three valet in the Monterey downtown Marriot basement parking and then driving 15 hours without shutting down to get back to Seattle.
Once home, I cleaned the electrical contact wire terminal to the solenoid and have never had a problem since!

 

most problems are simple if you look for them and work thru them methodically.

Impressed at driving for 15 hrs non stop, that takes some courage.

 

Another intermittent problem can be a "dead spot" on the starter. The solenoid will operate but the starter doesn't turn. The operation of the solenoid may move the starter over just enough that it will start the next time, or rocking the car in gear will move the starter enough that it will work.

One of those things to consider when you're doing your methodical work thru...

 

You've probably well sorted it now, but it's almost guaranteed that the starter pinion is picking up a little on the starter motor shaft so instead of inertia keeping it still so it screws into engagement with the flywheel, running to the end of the screw and start turning the flywheel, it just sits on the starter motor shaft spinning. I know from experience that you can live with this for "years" if you do not use the car often. A little clean and some lubrication on the starter motor shaft ought to fix it.

The other problem you might get is the pinion moving toward the fly wheel and then not engaging, but spinning and trying to engage. That's probably a combination of too much friction (again as before) on the starter shaft and/or worn teeth on the ring gear.