1987 tachometer trouble

Crank sensor would be what I would check next . If it gets hot and does the cranks but no start issue see if the tachometer registers while cranking it over .

This could be a bad tachometer signal filter.
Here is an inexpensive replacement. https://www.wc-autoparts.com/tachometer-signal-filter-camaro-firebird-fiero-corvette-gm-gmc-truck-monte-carlo/
Pretty easy to install.
The OEM signal filter have resistors and capacitors that dry out and go bad after 20 years. GM placed signal filter on most of there vehicles between the mid 1970's and the early 1990's.
The other item to check is the tachometer circuit board. They go bad as well. Here is an inexpensive replacement. https://www.wc-autoparts.com/1985-88-fiero-tachometer-circuit-board-ready-to-install-pre-calibrated/

Check for crushed/shorted wires.
Check part numbers to verify model compatibility.
If to no avail install aftermarket tachometer and turbo boost gauges.

You need to have the alternator checked. The tachometer runs off signal from the distributor, but can be indirectly affected by the charging system. It may be as simple as tightening the alternator belt, but I would guess that the alternator itself is going bad. Alternators that are marginal in charging ability anyway (old) may just go bad under the load of charging a fully dead battery.

Not sure about the tach, but the link should give you ideas to check on.
Do It Yourself Diagnosis and Repair

There's a good chance that the tachometer switch setting on the tachometer is broken. They use the same tach for different engine sizes and change the amount of cylinders with the switch. You might have to replace the tach

Check your engine mounts.

possible ignition coil itself because tachometer takes signal from ignition coil.you may also have check engine light on too.

its really easy im not to familiar with that vehicle but it all works the same if it hasd a distributer and a seperate coil or even a dis cap mounted coil either way there is two wires that run into that actual coil all you have to do is tap into them and figure out which way works just pull back the unsulation on the two wires that your tac will come with there might be 3 but one will be a ground and just kinda half way hook it up till you see the tac come to life its really easy just be patient and dont worry if the wires are wrong it wont blow anything up the tac just wont work until you hook it up right 9 times out of 10 when you buy a tach it comes with directions

I had the same problem with my 1995 Honda Accord V6 2.7L a year ago. It was a pain to have Honda diagnose the problem because it was intermittent and every time I took my car in to the dealership they said they couldn't reproduce the problem, but the longer you wait the more frequently your tachometer will fluctuate. I finally stopped by the dealership when the tachometer was jumping and they were able to diagnose the problem. In my case there was a faulty resistor in the ignition coil, but the entire ignition coil needs to be replaced. I don't know anything about cars but I know this fixed my problem. I went directly though Honda's service center so I know they charged me more than an independent repair shop but I'm looking at my invoice now and I paid $150 for the ignition coil and $200 for labor. After Honda diagnosed the problem I searched for "1995 honda accord ignition coil tachometer" and found that other people had the same problem and replacing the ignition coil was the fix. Hope this helps.