You have done all the tests correctly.

The leak appears to be somewhere outside of the fuse box and outside of the alternator.

This is quite uncommon. As mentioned above, the starter is one possibility.
The circuit diagram is required to determine what other items are powered directly from the battery, and not through the fuse box.

You must determine the source of this leakage in order to solve the battery drain problem.

The alternator may additionally be an issue if it is not charging. Have you tested the alternator while the vehicle is running? Simply check battery voltage with the engine turning at above 1200 rpm. The battery voltage should be in the area of 13.5 or so. If it reads 12V, then either the alternator or the regulator is not functioning correctly.

However, the combination of the faulty light and the discharged battery does seem to indicate a problem with the alternator. However, it is impossible for the alternator to discharge the battery if it is disconnected.