[rotorwrench]

Check all connections, not just grounds. I've seen terminal boxes fried to a crisp due to loose terminals inside. Loose connections create resistance and resistance creates heat. The only continuous loads on a model A are the lights and the coil. The coil will take around 4 amps in operation but it will only draw current when the points are closed so it goes on and off very rapidly. The battery can have deteriorating internal cell connections which can also cause resistance. See if the battery is warmer than normal after driving for a while. It should not get too hot. The coil shouldn't be overly warm either if it is functioning well.

A person can do current draw checks with the car shut down by watching the amp meter when you turn the lights on. The current draw should show on the amp meter as a discharge but go back to zero when the lights are off. This can be as high as 10-amps draw or more depending on light equipment configuration. If you turn on the ignition and the points are closed, there will be a current draw there too and it should be about 4-amps. If the points are open then there should be no draw at all.

Alternators regulate voltage & current depending on the needs of the battery since it helps carry the load. Once the alternator is on line during operation, there should be very little amount of current flow from the alternator to the battery after it reaches a fully charged state. It should only show a small amount of needle movement on a 20-amp meter but it will always show something toward the charge side.