Be sure to post the solution to the problem.

With the engine and key off, place a screw driver / piece of steel on the pulley end / other end of the alternator. If you feel it being pulled to the alternator, a diode is likely conducting in both directions ( shorted ). Just be sure the screwdriver isn't magnetized as it will affect the test.

A diode is a one way check valve for electricity, when it conducts in both directions the alternator windings remain energized draining the battery.

Another test is to use an amp clamp to probe wires looking for a drain. An Amp Clamp is a generic term for a mater that clips around a wire and measures current flow. If you get one, just be sure it will read DC ( battery for example ) and the lower cost ones only read AC ( house power for example ).

If you are tool limited, disconnect the battery then disconnect, insulate the alternator wires, then reconnect the battery and monitor battery voltage over time to see if there is still a draw.

There are other methods of testing but these are quick when limited on tools.