Before buying the switch, of course I was going to check if it was really b ad.
I took it apart and put a meter on it, and turned out I had voltage on the right output wires for wherever the switch was set. While I had it apart I hit it with a little contact cleaner.
So I put a meter between cord and socket. I had continuity to the center c ontact but not to the shell.
I disassembled the entire thing, kind of a pain, this thing is good German equipment solidly built, but more parts than necessary, and looked for a ba d connection somewhere, but nothing was obvious. Hmm. Looked closer, this has an isolated shell, and a separate lower tab that makes the side contac t. There was no voltage between center and shell, but there was between ce nter and side tab.
Aha. Problem solved. Bend both tabs for good contact, reassemble everythi ng, put the bulb back in and......
nothing.
Besides the bent tab, I had a bad new bulb. Got another bulb, now everythi ng works as designed.