I have a Chevrolet Lacetti where the base of the gear-stick vibrates when its in gear and the engine is revving, and the vibration causes a metallic "tizzing" sound.
If you rest your hand on the gear stick and move it just one or two millimeters, the noise can stop and come back.

I uploaded a video of the problem here: https://www.youtube.com/watch?v=PS3sPWRQt2k

It looks wet because I have just sprayed it with tonnes of white grease, which didn't make a difference.

Any idea how to sort this out? It's really annoying and is sometimes loud enough to drown out the radio and engine!