I have 242 tcase. This also applies to the Grand Cherokee tcases, and probably also applies to 231 & 241 tcases and any other tcase.
First I changed the transmission fluid in my 242 to synthetic transmission fluid. I used Mobil One tranny fluid and it help it shift a bit easier and run a lot quieter in 2wd and Full Time 4wd.
I suggest if your owner's manual calls for transmission fluid in tcase, use synthetic transmission fluid.
Yes, I'm aware that some later model tcases (like 241) come stock with synthetic transmission fluid. So for that tcase you've already got synthetic lube.
I suggest if your owner's manual calls for gear oil in your tcase, use synthetic gear oil of same viscosity specified in owner's manual.
I have experienced with my 96 XJ that synthetic tranny oil made my 242 shift easier (and run quieter) than with conventional oil. I think it also reduced wear.
Tire diameter makes a big difference in ease of shifting (for any tcase) and how quiet the tcase runs when in Full Time 4WD (for those tcases that have Full Time 4WD). Tire diameter also affects how much wear occurs when in 2wd or 4wd.
The goal is to have as close as possible to same tire diameter front and rear. So you need all 4 tires the same brand, model, size, load rating, and with a similar amount of tread-wear/tread-depth.
Assuming you have 4 identical tires, the next issue is tire pressure.
I have read some threads (at various forums) saying all 4 tires need same pressure. I have also read it's best to use 2 psi less in the rear tires.
I called a transmission shop and asked their opinion. They said all 4 tires need to be as close as possible to same diameter, and they said that would be with slightly less air pressure in rear tires than in front tires. They told me it'd probably be 2 or 3 psi less in rear tires for approx same tire diameter. They suggested I test it by trying different air pressures in rear tires and shifting tcase to learn when it shifts easiest into 4wd and back to 2wd.
I already had tested it in my 99 XJ with 242 tcase. (I have 30" tires) With 28 psi in all tires it shifts easily enough (I have synthetic oil in tcase). With 28 psi front, 26 psi rear, it shifts very
easily and runs very
quiet in 4wd Full Time. With 28 front, 25 rear, it shifts very
easily and runs very
quiet in 4wd Full Time.
I prefer 25 psi rear because in addition to shifting very
easy, it also has better ride quality, and quite a bit more rear wheel traction. With the increased rear wheel traction 2wd can handle the very steep gravel roads with ease. That's a convenience because I don't have to shift to 4wd for gravel roads.
The most important point is this, use whatever tire pressures front to rear that gives you the same tire diameter for all tires.
My Jeep (like most) is heavier in front, lighter in rear. So i need 2 to 3 psi less in the rear tires than front tires. This may differ for your Jeep depending on your weight distribution.
I suggest weighing your Jeep on a truck scale. Then you will know if you nees less psi in rear tires, and if so, use math to figure out how much less. Weigh with front tires only on scale. Then weigh with rear tires only on scale.
If you got your tire pressures right
(same diameter all tires), your tcase will shift very easily, especially if you also have synthetic lube in tcase.