A 12 volt draw on battery from a one wire alternator

You need to check the amperage of the draw. Not sure how you were checking it. You'll need to put an ammeter inline between the negative terminal of the battery and the negative cable. Anything over .050 amps is too much. If you have more than that you can start pulling fuses and then disconnecting connectors until the draw amount drops. You should use an ammeter that is fused incase it is a large draw so you don't burn up your meter.