Auto boxes have long been known to be at risk of exhibiting trouble after a fluid change when they are old and poorly maintained (and sometimes when well maintained). A transfer case and a diff are COMPLETELY different animals than an automatic transmission. Don't apply the "common sense" from one to the other.

 

Here is the critical statement in your post... "I don't like the way the transmission has been acting the past couple of days."

I would first check fluid level. Maybe it's low. If it's low, top if off. Report back? See if that helps.

I hate to break it to you but a fluid change probably isn't going to fix whatever issue you're having (aside from low fluid level causing problems). So ... you can try changing it... but I would bet you're looking at a replacement transmission, whether or not you change the fluid. I have never once had a transmission fluid change on an old ZF box like these help the transmission when it was already having problems.

On a properly working trans, yes, a slight improvement in shifting and smoothness but that's about it. I've never once *ever* had a fluid change fix a problem that had already started. Basically what others said above.

 

The next day, the truck drove just fine, actually. But still, I grew up in a world, where periodic partial transmission fluid changes were normal, not a controversy. Granted, that was mostly on Mercedes-Benz and BMW vehicles, but ZF is pretty much a BMW transmission, not only Jaguar and Land-Rover... )) Also, about 20 years ago I had a '99 Land Rover Discovery II and I did a complete transmission service/flush at a Land Rover shop, just above 100k miles on the clock. The truck ran fine ever since even after I sold it to a friend a few years later, and he traded it in a year or so later, no issues with transmission.
Having said that, I guess, I am supposed to check tranny level with the engine running but with the tranny barely worm, not hot? Which means I can't drive the truck to a work location and check the fluid unless it cools off. And it would take hours for it to cool off... Do I understand this correctly? I am confused.

 

@MyOldCars Hot or cold should not make too much of a difference,the engine is running so the pump is circulating fluid. If your truck sits for a couple hours you would be fine.