I finally made it to this room.
Either chip from the first area will work.
You can miss a switch in area 2 and two switches in area 3 and still get into this room, but those switches don't affect anything in this room.
The order of the switches doesn't matter, i.e. chip slot,
pillar switch, row switch,
or chip slot, row switch, pillar switch, or pillar switch, chip slot, row switch.
The only thing I could find out is that if, while fighting the Mystic and it's minions, you accidently shoot another of the row switches, the ceiling will make it's entrance without asking Mr. DeMille if it's time for it's close-up.
Otherwise I have not been able to duplicate this problem with Windows 7 and AlephOne file version 2015.6.20.
If you can get the switches to work, you can kill the Mystic's minions then with the staff lure the Mystic into chasing you around the pillar. Run into the little room behind the room and, again with the staff, activate another of the row switches. Since the staff has a pushback effect on Mystics, you can then keep it in the room while London bridge is falling down. Now,THAT's evil.