[LAYTON IS GONNA BE HERE A WHILE, MAN-- Sora even pulls out his notebook and tries to draw it out; one can practically see the gears turning in his head. and then he gets an idea. light bulb! it's a crazy idea, but it could... work?]

Maybe if you... turn on the first switch and leave it on for a while. Then turn on the second switch, but don't leave it on as long. Then you can go in the room and test to see how hot the bulbs are? The hottest one would be the first switch, the second hottest would be the second, and the cold one would be the third.