I had the same problem,I removed the tach from the steering column and removed the 3 screws holding the backshell on and I put some electrical tape on the circuit board where the board has holes for mounting to the shell, put it all back together and no more rattles,that was over a year ago and still good.

 

I bought torx wrenches from Harbor Freight for $10 because Advance Auto Parts didn't have a good one to lend. I unscrewed the tach, removed the shell, found out it was the red 'security' light that was a moving part. So I squeezed some glue in there and put it back together. Went for a test drive, problem solved. Will see how it does for the next week. Ugh had enough of the rattle, had to put up with it for way too long.

 

I might have to do this. Mine rattles first thing in the morning and is starting to drive me batty.

 

The electrical tape inside did the trick for me too.

 

For some pictures of how the tach comes apart, see:

https://www.northamericanmotoring.co...uge-mount.html

 

I know this is an old thread, but wanted to input my fix for this issue.
I used a thick, clear, doublestick tape from 3M, cut into small pieces to fit over the (3) holes where the black plastic cover screws in to the PC board.
No vibration or buzzing sounds since.