See that black cylinder in the lower left ? That's your tach amplifier. It's the reason your tach stopped working.
It's really easy to fix though, you just unscrew it, then pull off the top (that can be kind of tough, just pull); once you have it off, remove the tach amp from inside the casing.
Now find yourself a piece of foam, cardboard or the filter from a cigarette, and stick it in the case. Put the tach amp back in with the pins facing out, then screw it back onto the car.
Your tach will work now.
This works because the pins are floating in a was of silicone cement, and over time they aren't being pushed properly into the sockets of the part that mate with. By sticking a bit of stuff in the cap you're forcing the pins to be a bit lower where that actually make contact.
If this doesn't fix your amp, or more likely, you've had to do this a few times, then you either need to get a new tach amp from Beckman Instruments, or if you're adventurous you could try rebuilding yours. The electrics work, but the pins aren't making contact. I've never done this, but I suspect chipping away a bunch of the silicone and squirting some epoxy in there to anchor the pins might work.
Late breaking news: some dialectric grease applied to the pins seems to work longer and better when used on conjunction with the above quick fix.
Even later breaking news: after 4 years the tach amp finally failed and the tach needle would bounce all over the place no matter what. I finally got a new tach amp.
-- Richard Sexton