Hi Phil,
Mine normally acts like this;
I start the engine from cold and there's a small delay (seconds) between the engine starting and the alternator/ammeter showing a charge. It will flick from nothing up to maybe halfway although I suppose it could well go higher for a fraction of a second.
After a few seconds it settles down to maybe 1-2 amps (guess) with just a small positive deflection. If the battery is low it will obviously show charge for longer but at the moment I have a new alternator (17ACR) and battery which has a disconnect switch for when I'm not using the car so battery charge is good.
I can't say I've noticed great swings from the indicators when the engine is running but it should indicate some movement because ammeters are supposed to register all current in or out of the battery circuit. Unlike a voltmeter which is a fairly static thing and relatively slow to react, an ammeter is an instant reading so you could expect a pulse per "wink".
As long as it settles to zero or a small positive deflection you should be ok. The only caution I can think of is if you're getting a massive or continuous discharge reading then I'd be looking for a short. Likewise if it was continually charging despite the battery being good, then I'd be looking at the voltage regulator in the alternator, if you're getting 15 volts or thereabouts, it's over-charging.
AFAIK the voltage stabilizer is there for the fuel/temperature instruments, not the indicator circuit although I think they both have green colour wires & ignition fed. Are the gauges also showing erratic or no movement ?
Brian