Which alternator do you have, internal or external regulator? Either way, the only way it can drain the battery is for a diode to be leaking a little current, or the idiot light circuit isn't being broken with the switch off. Disconnect everything except the main charging lead on the back of the alternator, and see if the light goes out. I agree, it's probably a wiring problem. If you've got an internal-regulated alternator, you can check out the alternator by inserting a shorting clip into the D-shaped hole in the rear of the alternator, while it's running, and connecting the brush holder to ground. The alternator should go into full output. If it works that way, and not otherwise, the internal regulator is bad. Easy fix!
Jerry