I have had the same performance with an alternator in my Coupe. With the ignition on getting ready to start the engine, the ammeter shows a slight discharge because the ignition is drawing battery current. Starting the engine takes nearly 200 amps from the battery, so the alternator pegs the ammeter to full charge as it restores the battery. In a minute or two, the ammeter shows a slight charge as the alternator trickle charges the battery and runs the electrical system.
With the engine off, the alternator drew current from the battery because it has the wrong type of regulator for a single wire system. I put a diode in the wire alternator to terminal box wire to stop the current flow from the battery. However, I have to race the engine to get the alternator to turn on, so I know it has the wrong type of internal regulator for use in a Model "A".
I suggest that you take your car to an automotive electrical shop and have the alternator tested for operation and suitability for the Model A's single wire system.