A 12 volt draw on battery from a one wire alternator

BE CAREFUL checking current with a multimeter. Flukes have relatively expensive fuses, some of the inexpensive "Horrid Freight" have no fuses at all. The current measuring setup is a DIRECT SHORT between the probes, which means if you get that ACROSS 12V to round, "smoke will happen."

I would start like so:

Disconnect the battery for safety, the GROUND

Start by putting your 12V test lamp in SERIES between engine block and battery post. If it lights up fairly bright, you might have a fairly large draw and might damage your meter

Start with that, and post the model no. of your meter, we can step you through this