First thing I would try is putting a DC voltmeter on the battery terminals with the engine running and see if the voltage reads higher then it does without the engine running. That would tell you if it is trying to charge. I suppose it is possible that it is over charging shortening the battery life as well.
Should be roughly minimum 12V (12.6V full charge) not running and 13-15V running (full throttle) and charging.
If it seems to be charging then I would either put a DC ammeter inline with the positive wire to see if there is still current draw when the engine and switch are off. Or you could also disconnect the positive cable and measure resistance to the chassis ground with the switch off.
If you measure resistance or current draw in the off position of the switch, then you could start disconnecting plugs until the short/leakage stops to see where the problem is at.
Should be roughly minimum 12V (12.6V full charge) not running and 13-15V running (full throttle) and charging.
If it seems to be charging then I would either put a DC ammeter inline with the positive wire to see if there is still current draw when the engine and switch are off. Or you could also disconnect the positive cable and measure resistance to the chassis ground with the switch off.
If you measure resistance or current draw in the off position of the switch, then you could start disconnecting plugs until the short/leakage stops to see where the problem is at.