Shifter excessive shake & rattle question

free70

Thanks for the input guys.

On idle, I do feel a slight periodic pulse in the bottom of my seat (and the shifter shakes slightly in sync with this pulse), but I assume this is just the engine. At speed, its hard to notice if its in my seat or not (but I'll say no). I tried again on a new freshly paved smooth road, and it still occurs (as well as on the highway). On a regular "suburbs" street (i.e. not downtown full of potholes), the shaking is more obvious.

I took another video from birds eye view.
I'm not sure if its related, but the rattle that occurs is just as concerning for me now (I assume this is definitely not normal!).

https://youtu.be/jJFemOppwu8