Erratic Ammeter

My guess. The voltage regulator is supplying too much current to the field. Either because something is wrong with the regulator, or there is resistance in the circuit before the regulator. In either case, the result is the field supplies enough current that the alternator's output is 16 Volts. The battery will try to charge more when subjected to 16 volts, hence the current flow seen on the ammeter, but the actual result will be to cook the battery - boiling off the acid. The rapid ammeter movement makes me suspect the regulator itself.

Normal charging will be moderately high after start up, then dropping to zero after a few minutes of driving. What happens is the battery discharges during start. Once the engine is running, the alternator becomes the power source. As long as the alternator's voltage is higher than the battery's, current flows from the alternator. A portion goes to the battery until its fully charged. That's it. The ammeter only shows the portion going to the battery. As long as the alternator output is around 14 Volts, the battery will draw virtually nothing once its fully charged. The battery will temporarily read over 13 volts for a few seconds after the engine is turned off.

Where to begin?
I'd begin by taking a voltage reading at the input side of the voltage regulator. If its 14 volts, and the alternator is putting out 16 Volts, the problem is in the circuit. If both are 16 volts, I'd look in the voltage regulator.