First thing I would do if it were me is check the power to the clock/tach. Your service manual is your friend here and will give you wire colors and routing.
If there's power, you may have a couple issues. With the clock, as was mentioned, the usual problem is the coil. I had the one in my 300 rebuilt because I love to hear it tick and wind. That's just me....
The tach might just not be hooked up under the hood. They don't fail as often or fail completely like a clock. Wire hooks to negative side of coil.
The other possibility is the tach might not be working well with an electronic ignition system. I'll bet your car has been converted from points. Usually they work, but are not known to be accurate. They won't work at all with a MSD ignition.