[HighPlainsDrifter]

Hi,
Do you have an msd ignition box?
If so then the large capacitor in it is probably leaking / shorted / lower resistance than it should have.
I would suspect it as that is connected to the battery at all times.
Good Luck,
Perry.
ps- ammeter gauges that short out can cause a red hot wire and burn down the car, I would leave it disconnected or replaced with a voltage gauge.