Ok, thanks to the holiday, I actually got a day off and was able to look into the transfer case linkage on the Jeep. It's plenty rusty, but moves fine. I drove it around my back field and experimented with the 4 wheel drive. Maybe there's a smart person out there who can diagnose this...
While stopped, if I pull it into 4WH in an "aggressive manner" (basically, yank the snot out of the lever), the 4 wheel drive seems to work. It's noisy but works. After a few hundred feet or so, it seems to slip out of 4wd, the grinding noise starts and the jeep stops moving.
If I pull it into 4WH with less force on the lever, it doesn't engage and grinds when I let out the clutch.
If I perform the same aggressive engagement while rolling, it seems to stay in 4WH a little longer, but eventually slips out and starts to grind.
If I move the transfer lever over and pull up just a touch more (as if I we going for 4 wheel low), the transfer case ends up in neutral. Where I mention just a touch more, I mean a tiny amount of movement and it's no longer grinding and is in neutral.
4WL works fine and doesn't slip at all. It's actually a little less noisy than 4WH.
Are there any other 'experiments' than can be done to try and diagnose the root of the problem?
I'll also add that the 4 wheel drive indicator light on the dash doesn't light up.