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I have an 99 5.4L E350 dually cube van and have rear end noise when I back off the throttle partially.
I took drive shaft out ( all u joints and carrier bearing seems fine). I do have excess backlash in pinion gear. I can turn yoke about 1/8-1/4 of a turn and watch yoke come forward and back with back lash. It does not leak and it is full of lube.
put a socket on the pinion nut with a big breaker bar
these will take about 250 foot lbs IIRC
if it is not loose you will need to take the rear apart as
there are issues with your bearings