One of the electronic thingies inside is broken! (It IS April 1st)
Externally: if the point dwell were way off or the capacitor on the distributor were open, it would affect the tach reading. My experience is that the car will run badly if either of these conditions exist. Once you've determined it's not one of these two items, it's time to look inside.
Internally; It could be any of the little thingies inside. After 30+ years, some things are more suspect than others. The Schematics I have for BJ8 tachs show three capacitors. They are suspect. I would start by replacing the 100 uF capacitor, then the .25 uF (.1 on some units) and lastly the .47 cap across the piclkup transformer.
I'd say do all 3 at once, but if you're not profficient at soldering, wait a minute, if you're not comfortable working on electronic thingies, maybe you should send it to a specialist.
If you think the problem is internal and you are brave enough to want to troubleshoot it yourself, let me know, and I'll send you a PDF of the schematic.
Good luck, double check the dizzy capicitor.
Thom