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The next thing that is easiest to check is the connection to the distributor.
It's not unusual for the tach driver board to fail, but you have to remove the cluster to examine it. The used tach that I bought had a very obvious burned etch on the board. If you need a new one, buy one from Willcox. They re-designed the board so that it only uses 1 IC instead of the several used on reproduction boards (welcome to the 21st century). You could check the Willcox website to see if there are any troubleshooting procedures that you can do before removing the cluster.
BTW, the gauge illumination is a different circuit so whether that works or not will not affect the tach operation.
The tachometer on my 1978 does not work, I have checked the fuses, what should I check out next?
When you turn the key on, what does the tach do?
Does it go to zero, or is it showing a reading?
The tach on your car works off three things; power, ground and signal. If the tach is getting power and ground and if the board is good it will go to zero when the key is turned on. If this is what you are seeing, then go to the tach filter and bypass it.. see if the tach works.
See if the tach works. If it works then you need to replace the filter. If it fails to work then you should go to the pages listed below. I have a ton of info on the site on how to diagnosis your problem.