There’s always battery power at pin 2 of connector R347 (the luggage/cargo area light assembly in the Outback wagon).
It’s possible that the switch has been damaged, but I’m more inclined to think the BIU has, indeed, been affected, especially if the incorrect bulb connected the battery voltage at pin 2 directly to pin 3, which goes to the BIU. That terminal of the BIU is not designed to handle high current — the current through it is normally limited by the bulb. If the fuse to pin 2 blew, there would have been excess current (10 Amps), and that could well have fried the related part of the BIU.
If you can get to the three-wire connector R347 at the light assembly, and disconnect (might need to cut) the wire at pin 3 (red with blue stripe), and then see if the light stays on with the hatch closed, that could verify if the BIU is permanently grounding that terminal.
Also, if you have the assembly exposed, and have a multimeter, remove the 3-wire connector and use the multimeter to see if the switch is damaged. This can be done by measuring the resistance between pin 2 of the assembly connector and each of the other two pins. There should be continuity only when the switch is in the corresponding position. (Or, put differently, there should not be any continuity between pin 1 and pin 3.
