I’ve purchased a SYE and DC rear shaft.All TJs have a DC front drive shaft. I think they all have regular shafts in the rear. Even my 06 Rubicon has a single joint at the transfer case and a single joint at the rear pinion. So does the OP. Difference being his slides in and out of the transfer case, mine is bolted to the TC output flange. This is why people switch to a Slip Yoke Eliminater. And then buy a DC driveshaft. If they already came that way stock we wouldn't see so many vibration problems.
I wanted to take the rear out myself but my mechanic buddy said you might not be able to do that with an automatic. He knows cars that are automatic you can’t do that with.
Also if fluid comes out? Do I have to top up the fluid before driving?