Starting problem follow up
I first noticed that as I moved the shifter back and forth I could hear a relay click. That told me the NSS was doing its job.
I then hooked my voltmeter to the terminal on the starter solenoid and found that there was power there when the key was turned to the start position.
I used a screwdriver to tap on the solenoid and it started right up.
I promptly drove my Jeep to the barn and put it on the lift. I pulled the very muddy/greasy old starter off and replaced it with one from a ZJ that I am parting put.
Oddly the old starter tests fine now that it off the Jeep. I probably just needs a good cleaning. But after 295,000 mile it is probably due for a replacement. I will likely clean up the old one and keep it for a trail spare.