mine does this every now and again
not worked out why, hence everything below is a guess and suggestions based on that guess but it usually goes away when i
1) unplug and replug the connections in the chain up to the coil. i.e at ballast and to the coil bulkhead etc
2) arrange my plug leads so they don't run too near my electronic module or right across the coil mounting area on the engine block
3) blast out my igntion switch with contact cleaner (use one with lubricant, not circuit board cleaner)
potentially none of that fixes it
this started out as just the above apologies it got very long.. i was bored this morning.... this was the salve that maintained my sanity through 3 meetings 
but ultimately i think its due to an aged capacitor, in the guts of the tacho. capacitors can collapse inside and short out, and can also self heal when they get charged sympathetically up to a proper operating voltage again. I presume the action of disconnecting and reconnecting discharges a capacitor somewhere and it gets a chance to dig itself out of the error state it is in
depending on type, capacitors have a life, in years usually, 10 or so, or usage hours 3000 being the minimum for high voltage electrolytic used at their maximum heat and voltage capability (nobody does that, you always over specify based on usage)
can more or less guarantee that any in your car will be well past it
believe a tacho has a circuit to protect it and potentially 1/2 rectify the flyback pulses from the coil
and a timer circuit made from resistor and capacitor in order to do its rpm counting job.
and a circuit to drive the pointer and keep it steady.
A capacitor stores charge and a resistor dictates how fast that charge can flow in to it and back out again hence its a simple timer
When the tacho pins the pointer to the end stop, its ability to count pulses per unit of time has gone up the Swanee, which would suggest its ability to do timing aint busted, its just wrong due to the capacitor not working right. i.e the capacity of the capacitor has reduced due to collapse of its internals. it needs to self heal and un-collapse its inner gubbins
this is potentially caused by a fly back pules of massive size from the coil or alternator (both big coils of wire) when you switch on the ignition, due to the position of the points or trigger in dizzy or a fault with the ignition switch.
the action of turning the key can switch ignition coil or alternator on off on off on as you go from ON to Run to Start and back to Run. depending on how crap your ignition switch is, i mean it shouldn't do this, but dirty worn contacts play a part.... and every time it powers the coil up and down it tries to make a spark and will fire a pulse at the tacho.
a poor capacitor in the tacho can get abused by this.
this timer circuit also produces pulses in a tiny coil near a magnet that moves the pointer against a hair spring, and that pointer driving circuit will have an inductor (electro magent) in it to act as a damper to the signal, so the pointer doesn't BUZZ and vibrate and snap, it averages the pulses out to let the pointer stay still at a specific RPM otherwise it would just look like a blurrrrrr.
and finally the trouble is this tacho circuit will be potted in epoxy resin which will be rock hard so you can't see whats in the circuit, removing epoxy uses chemicals that will melt it and most of the circuit contained within.
Hence given the high cost of replacement for mine (Aussie/Mopar/ R/T tax) i haven't had the guts to investigate further...i'll leave that until it properly dies
Try switching on with the points disconnected
or the coil diconnected
or the alternator disconnected
see if the tacho stays at zero.
insulate any disconnected wire to avoid sparks
that would help point to maybe igntion switch/coil or alternator blasting the tacho and causing a capacitor short
if one of them is
a zenner diode in the lead to the tacho may help
1 end to coil - and crimp on a connector to the other end so you can plug in the tacho wire
wrap in cling tape or cover in heat shrink
you will have to try it 1 way and then the other, a diode is a directional device that stops current 1 way and lets it flow the other, and i can't remember which way round it needs to be.
wrong way round and the tacho won't work.
IN4004 zenner diode would be ok but get one, good for say 400V cost about 30p worth a try
we don't know which way the errant pluse is going, so this guards against backward stuff hitting the tacho, a sure fire way to collapse the internals of a capacitor is to hit it with a voltage going the wrong way.. this is why many have the negative lead marked with a -
the diode allows the GODD but stops the BAD and the UGLY
Dave
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