Vibration comes in two basic forms. Plain old shaking and harmonics. Harmonics are related to something reacting to the primary vibration and reacting with a secondary vibration. If you want to see it in action, open the top of a piano and shout into it and listen to the piano answering back.
Harmonics vary with the resonant frequency, in this case the rpm of the engine and the rpm of the wheels. Your tach could be smooth as glass at 7,000 rpm and shake like a mother at 8,000. If you put a vibration analyzer on the frame you would see multiple peaks as you raise the rpm. Small changes affect it. Bolting a small piece of lead weight will change the frequency. Lead dampens everything. Tuning problems with carburetors is sometimes related to severe vibration. I fixed a persistent tuning problem on a Triumph dirt tracker with solder wrapped around the carb.
I would use a digital tach and skip the mechanical version.
Trying to analyze it to come up with a solution is a huge waste of time. There are tons of commercial vibration isolators that were designed by engineers.
Bolt it solid? Guaranteed to destroy it. Not just the tach, but everything electronic. Everything.
The Lord corporation makes a gazillion different products.
http://www.lord.com/Home/ProductsServices/VibrationShockMotionControlProducts/tabid/3280/Default.aspx