Just an idea here. On the back wall of the cab you have one or two ~6"x6" vents that face the bed and are only 1.5-2" away from it. When you close the door a lot of air is forced through those vents. I surmise you either have a loose vent rattling or banging, something foreign in the vent or between the cab/bed impacted by that moving air, or you might have something loose on the front wall of the bed and enough air is shaking it.
There was another post you can search on where someone was complaining about a missing weld or something similar that led to a very flexible top front rail on the bed. Maybe this will help narrowing it down.
