Thanks for your various suggestions. I will certainly try the simple things first. As for a voltage spike, I can't think of having had one, but shortly before the tach stopped working I did burn up my alternator belt and replace it. Am I correct in thinking that the tach leads attach to the alternator somewhere? In that case they may have gotten pulled off in the tussle.
Question for Sander06: How do I "check the ground?" (I'm just posting this question to help others out there who might not know the answer, not because I would be so ignorant myself