Time to measure back lash. Should be between .006 and .010. Make sure you check and measure in at least three different places.
If you haven't done this before you measure the movement by holding the pinion flange so it doesn't move. Then with your other hand measure the distance the ring gear moves from tooth to tooth or the slack. If it is too much you will have to adjust the shims on the left and right of the carrier.
If it is too tight then you need to add shim to the right and take equally from the left.
If it is too loose then you need to add shim to the left and take equally from the right.
Normally it is a one to one ratio. If your backlash is .001 either way take or add .001 from your shim size.
Again, Fords were very different and you almost always had to adjust a little but I guess Jeeps build their R&P to tighter specifications and if staying with stock then you should be pretty close. I stuck with Superior (as they warrantied my part) and the measurement was just right.
From here you check your wear pattern. This is how you tell if your pinion has the right depth. You should check both sides for by the book answer. But mostly the important part is the inside curve (concave?)
You want the wear to be pretty much centered. To do so hold the pinion flange firmly while rotating the carrier. It is a special compound that is used... gear marking compound... and you just rub it on the gear sets. Fairly easy stuff.
Reconnect your sensor by pushing the wires through the hole in the back left.
goes to this little thing, if you broke the tab earlier don't worry too much. I have been told that there is enough natural friction to keep it from popping out.
Everything all buttoned up.
Make sure you clean the mating surfaces of the diff and the diff cover.
Now just add your diff cover. There is no need to put excessive amounts of silicone sealant on it. Just a little is all that is needed. I like to rub it around to make sure I get good coverage.