tach question????

My wife and I recently a 97 GMC 1500 Suburban and the tachometer isn't working. When you start the engine it goes to 3800 RPM and stays there, but drops to zero (slowly) when you shut it off. The wiring diagram says there is a white wire from the distributor to the tach. I've checked the connection at the distributor and it's OK. I'm guessing that it is the tach itself but I was wondering if anyone else has heard of a problem like this before? I called the dealer and and they said the tach is not a replacable part, that the entire cluster needs to replaced at a cost of $445 for the cluster...no labor.

Thanks,
Dave