I think what druid is saying is the problem if you don't find that the compressor is it. 3 amps is about what an Alternator will pull back through itself if left on.
The little green box looks to be a relay. Does one of the wire off of that "y" go to it?
Yes, it connects to the wire that oes to the warning light and to the relay.
The one wire (black I believe) that is coming off of the main lug on the alternator is hot as it goes to the batteries. That wire goes to the "Y", correct?
Yes, it had what I believe is a diode on it.
At the "Y" junction one wire goes to the alternator and it should not go to the field (F) terminal as far as I'm concerned.
OK, what are you calling the field (F) terminal? the red wire? If so, it is connected I think to the D+, or warning light terminal. You are right in that with just the two wires from the y connected, and not connected to the other side at all, the 3 amp draw is present. But that being said, this is how it was connected before I removed the alternator to take to the shop.
It has been ok for the last two or three years since I had the alternator rebuilt. I have tried to think that maybe I did not label my diagram right before removal, but I can not see any other way that it could be connected. Notice that there is also a black wire from the negative terminal that goes direct to the relay with another wire that jumpers the "switch" side of the relay.
If you have a wire to the field it has to be switched or it will drain like you are saying is happening. Normally there is a wire through and ignition switch that goes to the field wire.
One wire should go from the battery side of the alternator to one of those spades (not the field one), but I can't see how they are labeled.
They are not labeled as far as I can see with the alternator in my lap and a magnifying glass to aid vision.

There are two wide spades and a narrower one. The red wire is connected to the narrow one...spade would not allow it to fit on the other 2.
The field one will help to energize the alternator and make it charge at low rpm's. Usually you don't need it if you rev the motor over a couple thousand rpm and get it energized that way.
I'm wondering if somewhere along the way the wire going to the spade terminals is not on the right one and if it is on the Field it will probably drain the battery.
I also wonder about the purpose of the relay in the picture and if that isn't involved with this.
I do not believe it is the relay in the wiring diagram. I suspect that it was added to run the clutch compressor, a Saden S505 I believe. The green and white wire connected to it goes up to not the compressor, but another part of the refridge system.
c ya,
Sum