Shifter movement on the throttle

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Hi all, new Z owner here and am loving it except for one annoyance: I can feel the shifter move slightly as I get on or let off the throttle. There's also quite a bit of vibration in the shifter overall, even if I'm just sitting idle in neutral.

Now I've read up on clutch "shudder" or "chatter" -- my experience isn't with unexpected sounds or anything, just the vibration and movement of the shifter that I don't think is normal.

Am I off my rocker or should I take it in? I've got a 2011 Touring with a little over 1200 miles on it...