Hi,
The idea that it does it in reverse leads me to believe it could be related to a bad engine mount. Do me a favor. In a safe place, park on a flat surface. Open the hood, apply the parking brake, and then have a helper start the engine. Have the helper place the vehicle in reverse and hold his foot on the brake and apply a small amount of throttle to load the engine. While that happens, watch the engine to see if it moves more than seems normal. Pay attention to when it shifts from park to reverse to see movement. Also, do the same in drive to see. Just don't get in the way of the vehicle when checking. I don't need you to be run over in the event the brake fails. LOL
You can record it and upload it for me to see.
Here is a link that describes motor mounts:
https://www.2carpros.com/articles/how-a-motor-mount-works
Let me know what you find or if you have other questions.
Take care and God Bless,
Joe
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Monday, March 1st, 2021 AT 7:46 PM