UPDATE 1 -- Replacing rear bearings on a Dodge pickup?

You removed the weight from that side, thus most of the load from the bearing. With the wheel spinning the brakes shouldn't come into play. If you removed the drum easily, they doubtfully are in contact. Try spinning the noisy side by hand. You may hear it or feel a bit of play up and down.

Roy

Roy, I tried something else with that right side.

I put back the drum and wheel. The noise resumed.

Then I took off wheel, kept the drum. (used wheel lug nuts to keep the drum on). The noise continued identically.

I took off the drum, tried running again. NO noise.

I put the drum back on again (you can see that I like redundancy). The noise resumed.

The drum does not weigh much, just maybe 20 lbs. The wheel is obviously a lot heavier, maybe 50 lbs.

I think that it is unlikely that the weight of the drum is the issue

-- though I will try with a wheel on without the drum.

IIrc this started as a noise and a vibration that was felt under your feet. It is doubtful that the brake drum is causing this. But never say never. Switch drums from side to side to satisfy yourself. The shoes aren't showing abnormal wear are they?

Roy

No, they are not showing that.

I tried one last thing. I put on a rear wheel WITHOUT THE DRUM. (also attached using lugnuts)

The noise, much to my surprise and disappointment, resumed with the wheel and NO drum.

As a extra info, there is indeed play in both rear bearings, my wild guess would be 1/2 mm. when i try to move the hub up or down.

It would seem you have identified your problem. I believe you have a manual. Just follow along, not a horrible job. You'll need a machine shop to r&r the bearings. Check the housing for damage as well as the axle. I'm outa here for a few hours.The others will help if you run into problems.

Roy

Thanks. I will buy new bearings from a dealer today. I made some pictures also, and opened up my differential, see my another post.