Other things I've seen that have caused this:
1) Bad ground at the relay bracket. The ground wire for the ignition box connects to the rearward screw for the relay bracket on the driver's inner fender underhood. If this is the case, when the tach drops to zero, depress the clutch and see if the car seems to be running around 1500-1800 rpm or so (or if it dies).
2) Shorted small clock harness - usually causes weirdness like this if the lights are turned on, eventually will also cause the fuel and temp gauges to go crazy, then smoke to start coming out from behind the cluster. Happened to me on an '84 245GL that a VDO-branded clock was installed in. Wires were melted together afterward, and I also had to replace the circuit board on the back of the cluster. Tach worked fine afterward, but could not provide power to a clock, since the clock harness plug traces were cooked - I actually have this tach in my 242. Still works fine, but I use my radio's built-in clock. Partly because I have no room for a 52mm clock, unless I get the 1394000-2 gauge pod or delete my heater vents.
3) Loose solder joints on the cluster circuit board where the round harness plug attaches.
4) Corroded fuse 13. Typically will be more likely to just shut off the cluster, leaving the alternator charging light on while the car's running. More of a problem on 1984-on cars, since it seems that earlier cars will just die if the fuse stops providing power.
5) Impulse sender in the distributor. Usually, though, when the tach drops to zero, the engine will stop running as well.
Easiest thing to check is to see if the tach's board has a failed component or bad solder joints, though. Luckily, all 1981-93 tachometers will work. Some may not match the cluster perfectly, since the 6500 rpm redline tachometers seem to have a glossy face, most 6000 rpm redline versions will be satin face, except for some early V6 versions that will also be glossy, and the 1989-on matte tachometers. I had a tach from an '88 245GL in my old '84 245Ti. Worked fine. Just didn't have that 5500-6000 rpm boxed in region. The tach I have in my 242 is a 6500 rpm unit from the aforementioned '84 245GL.
