Well, Dan, you might want to clean the contacts inside the plug that plugs into the tach assembly and the mating pins up inside the tach housing. These things are known for plug-together electrical connections getting a bit crusty with age.
But, you say the tach "doesn't work" and also that "the tach needle bounces". Which is it?
Welcome aboard, seems the percentage of LS bikes is rising quicker than the standard ones!