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In what way does the "rear end" "drop down"? Are you talking about the rear of the car squatting on acceleration? Or is perhaps the front of the axle housing itself (the pinion end) pitching downward...?
Putting it in reverse sure doesn't sound like acceleration squat then. But I still can't tell if you're talking about the rear of *the car*, meaning the trunk/bumper/body, or if you're using "rear end" to refer to the axle assembly itself. For all I know you might mean the rear end of the driveshaft. Can you post a video link showing what it's doing?