Ok, I looked at the switch - the metal part (sleeve) in the middle is a part of the switch itself, it's attached inside to the round plate with contacts that rotates when you turn on the switch. And that metal sleeve has indents on the inside surface that are supposed to hold a bulb (at least I believe so).
Maybe it's not an original '39 switch? There are no numbers on it, just some words "Boston, Massachussets, patent pending".
I'm stuck.