There's a good chance it's your rear diff AND bad rear wheel bearings.
The "wobble test" is simply jacking your rear wheels off the ground, and shaking them up/down and side/side...seeing if there's any play. It's an easy way to check for failed bearings. If there is any wobble or play, they are bad. However...if they feel solid, they may still be bad...but the rear hubs would have to be pulled. But any play at all, and they are for sure bad.
You have two different sounds there. You have the whine which is 100% coming from the differential. You also have what sounds like a roar in there which is what the bad wheel bearings sound like on these.
About the only thing you can do right now with your rear diff to try and quiet it down, is drain all of the diff fluid, and replace it with a 75w - 140 synthetic fluid, and ADD extra friction modifier. Depending on what auto parts store you have in your area, all they had in mine was Mobil1 75w - 140 and some little bottle of CRC brand friction modifier (comes in like a 4oz bottle). This did not help my diff whine at all. My diff was completely rebuilt at 60k miles by Ford because of the diff whine, and it reappeared at 100k. I'm now at 134k with the same whine, and it will just have to stay that way.
In the coming couple of months when it warms up, I am going to drain my diff again and try a better diff fluid. Either Royal Purple or Lucas, and see if that clears it up. Some people report that their whine went away with these brands, as the Mobil1 did absolutely nothing for me. What you're hearing back there is the differential clutch pack and ring/pinion noise. They wear quickly on these trucks...and it's all too common.
So my 2 suggestions to you, for both of these issues is:
#1 Jack up the rear end, one side at a time is fine. Try to wobble that wheel all around. If there is play, you have bad bearings.
#2 Drain and replace the rear diff fluid with a 75w - 140, quality brand. If you only have access to Mobil1...try it out, it's about $15-$18 a quart and you will need 2 of them, plus the extra friction modifier. The diff only takes about 1.5 quarts to fill. If you have access to something better like Royal Purple or Lucas, spend the extra $$ on it....
If you change the rear diff fluid and you still have the sound, you need to decide if you want to just live with the annoyance that is there, or go spend a hefty sum of $$ on having the rear diff rebuilt (new clutch pack and ring/pinion). It will be at least $1000, and that's being conservative.
You definitely have diff whine, 100% without a doubt.
Good job uploading the video. What the hell crashed back there at 35 seconds, lol
)
and I'll try the wobble test soon-- my parents are gonna take it to the dealership next week I think :/.
