Originally Posted by Edward Wyatt

A bad diode or two in the alternator can cause the battery drain, I sure hope the "mechanic" didn't hook the battery up backwards for a second or two because the end result is a fried alternator such as you likely have.

The light in the cluster is what energizes the field, if a doesn't go out that means it's not generating any current, the diodes prevent current from bleeding out of the battery and to the alternator when the engine is stopped. They are a one way valve of sorts, but they don't like reverse polarity at all.

The key here is that the light won't go off since the battery was replaced, the only thing that would cause that would be reverse polarity.

The alternator has a large wire on the back that is always hot, even when the car is off. That is the conduit through which your battery is being drained via the bad diodes.