Quote Originally Posted by GameFAQS
You would first enter a battle where you have to fight 2 Dual Horns and 1 Guado. Then descend down the stairs and when the screen shifts, go back up the stairs. Proceed through the hallway and enter the Quarters to the left. Win the battle there against 2 Dual Horns and 1 Guado, and search near the bed for it or to the right of the right-most chest. It's in the same room with the two Al Bhed password-protected chests.
I guess it's in the al bhed quarters, meaning you've missed it if you're past that point.