I’m working in rehabbing a machine very similar to yours. You’re a bit ahead of me. I took my headlamp apart a few days ago. I made a sketch of the wires that I don’t have in front of me. I recall one of the whites being on a different terminal. I think the switch’s double tab had the 2 wires sharing spade; one of the single whites was on the back. That would conflict with the diagram but I’ll look when I get home.
Did you happen to snap a picture of how the spring clips hold the glass in? I took them out recklessly.