Which Engine? I looked up 1988 E350 XL Trim with 460V8 and found
The thing on top that looks like a door stop is not exactly a solenoid. For years, Ford had part of the field assembly rigged up to pull in magnetically when the starter energized. It engages the Drive but does not energize the starter like the solenoid on most other manufacturers' starters.
The Solenoid looks more like this
It's located in the fender liner. Is this the solenoid you're working on? If so, what's the other?
The parts look to be same as we had on our 1983 E350 460V8. I had access to a pile of parts plus a helpful auto electrician. Built several starters for it with his help. Sometimes it was Brushes or Bearings (bronze sleeves) but I also had a Field Winding fail Shorted and an Armature fail Open.
Of course they won't crank if the Brushes have failed and they're available for about $10
It's an easy starter to remove (two bolts and one cable connection) and test (ground clamp to housing, positive clamp to the cable connection and it should spin). It's just heavy.
But check your Battery and Cable Connections first. And not just the Hot side. Check the Ground Cable too.