Despite its fancy name a periosteal elevator appears to be more or less a little spatula or butter-knife-looking thing usually used to move brain tissue around. James Watts, Walter's partner in prefrontal lobotomy, used it to cut nerve fibers, finding it more precise than a leucotome. I wouldn't know about that.
You don't hear a lot about James Watts, possibly because he broke up with Walter after Walter started going in through the eyes. James didn't approve of that and he especially didn't approve of it when the guy doing it wasn't even a neurosurgeon, just a very enthusiastic psychiatrist with an ice pick. James himself was a real hotshot. One of his psychosurgical party tricks was measuring a patient's brain by threading a wire through it. But when you're Walter Freeman's partner it doesn't matter what you can do, he's always going to hog the limelight. He even gets credit for lobotomizing Rosemary Kennedy, when it was James who was swinging the periosteal elevator. Walter was just peering into her skull telling him where to aim the thing.
Incidentally, did you know that myrrh is an embalming spice? That was the significance of the third wise man's gift. I think that puts the Killian periosteal elevator into perspective.