Never found it...

when working your way out of the asylum, an apparition arrives and quizes you. At one point he brings you to a room with a bunch of other apparitions that ask a bunch of questions when you talk to them. Before talking to them, check out the table they sit around, it's there....

Not sure if you're talking about the cloak of reflection or the cloak of mirroring, they get mixed up a lot. The reflection cloak reflects electricity, the mirroring cloak reflects anything. The former is in the place Zenith said; the latter is in the Sahauguin (uh, forget how to spell that) city. Go to the place with the big face and step on the circle, and a bunch of Sahauguin will appear and attack you. One of them has the cloak of mirroring.