Model originally uploaded to Thingiverse at https://www.thingiverse.com/thing:4375458.
Attention, there is V2 as when I was designing this I didn't think about some stuff so I added them, but I didn't print this updated model. I'm only unsure about the switch if the top cover will fit as I think it should.
Features: Battery operation, built in charger, battery state of charge, adjustable brightness, adjustable lamp length.
Links made by Teaching Tech https://www.thingiverse.com/thing:3223979
Print settings: 0.4/0.6 nozzle, 0.2 layer height Supports recommended for lampMount and LampTop Print as oriented from the files.
Things that came up during assembly that I didn't think about when designing: No ON/OFF battery cutoff, the boost converter will drain the battery slowly. Unable to see when the battery is charged (is visible from the rear only)
The ⌀ 4mm holes of the webcam mount are too small for any connector to pass through. You won't be able to change the number of links without removing the connector.
I've also uploaded a updated version that I didn't print out, so I'm not 100% sure that it will fit, but it incorporates some fixes:
Changed M10 thread to M12 for the holder and enlarged the hole to ⌀ 8mm (2 pin XH connector should be able to pass). Added mount for a switch in the rear (10×15 SPST KCD11).
As always, step files included.