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Just a question, would a bad or wayward tach filter cause the tach to drop to zero after reaching 3600 rpm but work below that rpm level all the time? I have ‘87 vette.
The "filter" is an electrolytic capacitor, and when they deteriorate (over time) they can short out.
I can't say this is what is causing your problem, and I don't usually suggest replacing parts unless their function (or lack thereof) can be verified by measurement. But, in this case, these "filters" are so inexpensive and simple, they are the exception to the rule. Go ahead and replace it and see if that fixes the problem first.
If that doesn't do it, BATEE can service the cluster for you.