Ok, I guess I got a little carried away, but here's what I would do if it were my pick-up ...in this order:
1) Perform a Swerve-Test. That is, drive it where you can hear the noise, then swerve left, then swoop right in long swooping curves and note if the sound is slightly louder or worse one direction or the other. Probably goes away when the load is reduced on a particular side.
2) Do the emergency brake test. If your truck allows ....when you hear the noise, depress the emergency brake a smidge ..then a little more ..and listen if the noise is reduced. Don't continue to drive with the E-brake on... just do is w/o driving very var like that. It's just a test. The theory here is the brake shoes inside the rear drum (rotor) will center the wheel and remove some of the weight off a rear wheel...enough to reduce the noise -- if that's where the noise is eminating from. If you hear the noise reduced as you do this, then it's probably a rear wheel bearing. But if not, then it may be elsewhere (it could still be the rear wheel bearing though).
3) Check front wheel bearings/hubs: Sometimes sounds can 'seem' like they're coming from the rear, but might not be. With the front raised, wiggle each wheel vigorously withh your hands in the 12:00 - 6:00 position. There should be NO movement.
4) Listen to Front Bearings: Using a long wooden stick (like a broomhandle), run the front wheels (vehicle on jackstands), and put one end of the stick to the bearing region of the front spindle, the other end to your ear. Press the wood stick against your hear kind of hard. You can literally "Hear" the bearings inside. If you detect roughness, grinding, etc, then you know that's the one. Even if they 'feel' tight, they could be grinding inside if a bearing has a chip, flat-spot, or the inner spacer is coming apart.
5) Driveshaft Center Bearing: If your pickup has a center rear driveshaft support bearing, push up/down on the center bearing, feeling for freeplay ...and rotate the driveshaft (trans in N). Might even want to do the wood stick test on and listen to that bearing. They DO fail, and can howl.
6) Rear Axle Bearing Test: Lift up on each rear axle (vehicle on jackstands). Best if you remove the wheels first. The axle rides on the raw bearing rollers (like a GM axle) ...so if there's wear you may feel some up/down movement. But ....if you have it up on jackstands with the wheels off, and you're considering removing the rear cover anyway (esp if you don't find the problem with the front wheel bearings), why not spend a couple easy minutes and pop out the axles and have a good look? You could have some spalling going on the axle surface, and it might not show up by lifting up/down on the axles.
Hint: Before you pull out the rear axles (but have the vehicle supported, wheels off), inspect the rear gears by eye and rotate the Pinion (by hand -- rear driveshaft unhooked). If you feel some 'roughness' or grinding ...it probably indicates a pinion bearing going out. By doing this step BEFORE you remove the axles, you won't have to worry about the spider gears falling out ...and having to waste time working them back in place. After you've done this, then pull out the axles and check the axle bearing surfaces and bearings. If it looks good, I would pull out the rear bearing seals and install new Mopar ones (since you're there). Or bearings if you detected free-play. Otherwise, rear wheel bearings can go 200k+ mi (probably 300k+ if you don't tow/haul much) ...so if they seem 'good', no reason to replace a good OEM bearing with el-cheapo Parts Store bearings.
7) Driveshafts/U-joints/CV's: While you're at it, inspect all these. It would be a good idea to remove the rear driveshaft U-joint, put the tranny in N, and feel the bearing caps for 'roughness' and the center bearing for play and also 'roughness'. You may want to pull off the rear U-joint end-caps and inspect the trunnions for fluting, etc. Same with the front D/S ...or at least rotate and push/pull to inspect free-play on the splines and joints . Inspect the tranny output by pushing up/down at the rear driveshaft to inspect the 'freeplay' at the back of the tranny. There may be a minor amount, but not much (that bushing can be easily changed if needed by the dealer). Inspect the front CV half-shafts as well.
8: Conclusion. If you go about it as described above, you should uncover the problem and may even find a few future 'potential problems' fairly quickly which you or a mechanic can get on, and avoid an on-road *situation*.
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