Yes. There was one in the drawer. I did use it one morning and it worked well.
Yes I hink they are in draws.
Yes, they are oddly placed away from the bathroom and near the writing desk, but they are in the room. Also, the lighting switches are British backwards, you will see what I mean.
All in all, I think you will see this as Edinburgh's version of "Faulty Towers" and walk away with some humorous memories.
Get an answer from The Old Waverley Hotel staff and past guests.