I guess I'm not sure what you mean by the big red button...
Testing vibrations while running motors on a flat surface isn't very useful. The turbulence from the props will cause all sorts of shaking. Ground test are more useful on individual motors, when they can be held over an open area. Of course with the right rig, one could do it, but as Jd points out, that only gives you the overall vibration level, which can probably better be deduced from a flight anyway.
I'm generally seeing that if my accels have more than ~0.3 range of noise, then the AQ PIDs need to be tuned down to compensate. That's very general. Some vibes are more obvious on the XY and some on the Z. I haven't been able to make much use of the gyro plots, though I'm sure with more experience one can get useful info out of them.
Actually I have a good example for you... Here are 2 log graphs from the same Y6, same day. The difference is I switched props for the 2nd flight. Both sets were balanced in the same fashion, on their own, not dynamically on the motors. Tilt Rate D is 7180. The first flight was very smooth. The 2nd flight had very noticeable instability... the motors ran less evenly, and altitude was harder to maintain. Also very obvious by looking at the MOT_ROLL and PITCH graphs that the motors were working harder, with more speed variations and range. I cold probably tune it out by lowering TRD, but that's obviously not the best solution.
Smooth:
Rough:
Any questions?
HTH,
-Max