okay, i just checked out the video and yeah, it looks like your pinion nut is loose. you'll need to use an 8mm socket to remove the bolts securing the driveshaft to the pinion flange and then, pull the base of it out. once removed, you should be able to see the pinion nut. if i recall, you'll need a 1-1/4" socket to tighten it but here's the trick, while the torque setting for this is 160-200 ft. lbs., there is a crush sleeve that may get crushed more and put more pressure on your pinion bearings and that will ultimately cause them to fail prematurely. being that you are getting rid of your jeep, i would remove the nut, apply some red lock tite to it and then just tighten it back to 160 ft lbs or there abouts. this should hold things in place.
