Thanks.
The car has been sitting for some time and was not running when it was parked. So, it's difficult to know whether something could have been tampered with. I know that the radio was tampered with, and there is evidence from removing some of the panels that they have definitely been removed before. However, I have no idea how long this has been a problem since this car is new to me.
I was hoping for a more simple fix, but if it's a bad tach-- that's just what it is!

It isn't necessary, just nice to have. Thanks for the suggestions.