Got 'er done! About as easy as any clean-up of an old tool I've done lately.
I have a feeling I'm not the first one to re-wire this light:
How long has the silver screw/gold screw standard been around?
There is nothing to provide a strain relief on this vintage light, so may as well go vintage:
A fiber gasket from a CO2 canister and an Underwriter's knot to the rescue.
Back together:
I have no idea what the paint is (copper plating? I don't think so.), but it survived a half-hour in an industrial ultrasonic cleaner with 180 degree F lye solution, so I chose not to re-paint. I gave it a good coat of Renaissance wax to keep any further rust off and we'll just call it "patina". I also have no idea of how old this light is, but that home-made reflector is NOT galvanized--it's tinned! I haven't seen tinned flashing in a while.
The cage is retained by four captive thumbscrews that fit into the keyholes--very easy to remove to replace the bulb. There are two currently unused, smaller keyholes that I think were to mount a (missing) retainer for the bulb base.
I just happen to have some LED "Edison" bulbs around, so:
Now it's Steampunk.
I have a fabric-wrapped vintage lamp cord on the way. It's only twelve feet long (and only cost twelve bucks), but I won't really be using this much as a droplight (I'll probably be eating those words) as I use a headlamp for all that kind of stuff these days.