https://youtu.be/PnVz9L5g4pQ
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I too have a thing for old lamps; a little refurbish and LED bulb makes them equal most available new.
And won't burn your forehead!
One add for viewers though, didn't surface in video and seems insignificant to some.
In the name of electrical safety;
Re-establish polarity of plug, wire, switch and socket with this sort of project.
1] Smooth side of duplex wire is hot. Ribbed [or white insulation] side, neutral.
2] The plug, hot is smaller prong, the wider is neutral. This applies to receptacles as well.
3] Socket hot wire connects tit at the bottom of bulb, bulb shell [the screw] is neutral.
4] If switch is separate, of two screws available, unplated is hot. The silver [signifying white] is neutral. Job of a switch or disconnect isolates [breaks] flow of current. Sure, it'll work the other way. Just let mother-in-law change bulbs.
This arrangement insures fixture is fully OFF when selected; not directing power over the switch, rendering the assembly always hot.
Old plugs can be reused, but have equal blades; being made before polarity, continuity and grounding of housewares came under UL [Underwriters Laboratories].
UL, NEC, NFPA, FM, UPC and other Uniform Codes; written by tradesmen and real engineers. AFAIC, the thinking mans OHSA, sans administrative tangles.