Entirely by accident, I discovered that engraving a hairline with LightBurn’s Dot Mode using 1 ms burns and 0.1 mm spacing produces a continuous trench, rather than the series of dots at 0.25 mm:

The left is at 20% power (12-ish W) and the right is at 30% (18-ish W), both filled with Pro Sharpie red ink.
The V-shaped groove is even more obvious when seen end-on:

In both cases, the travel speed seems to be about 10 mm/s regardless of the speed set in the cut layer parameters. The higher power level produces a slightly wider cut that doesn’t seem deeper, which I cannot explain.
Filled with red lacquer crayon, the hairline looks absolutely gorgeous:

Engraving the PETG sheet with the protective film in place produces a neat cut with the film edges fused to the plastic.
Cutting the outline and pivot hole in the same operation ensures everything remains perfectly aligned:

Scribble red crayon over the film, make sure the trench is completely filled, peel the film off with some attention to not smearing the pigment, and it’s about as good a hairline as you (well, I) could ask for:

The pigment in the trench is about 0.2 mm wide, with slight heat distortion along each side, and I’ll call it Plenty Good Enough.
Totally did not expect this!
Getting a good-looking hairline on a good-looking cursor turns out to be a major challenge, because there’s nowhere to hide the blunders. A few of the many dead ends along the way shows what’s involved:
https://softsolder.com/2020/05/06/tek-circuit-computer-cursor-hairline-scraping/
https://softsolder.com/2021/01/26/tek-circuit-computer-cursor-hairline/
https://softsolder.com/2021/02/16/tek-circuit-computer-sawed-hairline-fixture/
https://softsolder.com/2021/04/13/tek-cc-milled-cursor-vs-speed-vs-coolant/
https://softsolder.com/2021/04/15/tek-cc-milled-cursor-mvp/
Plenty of Quality Shop Time™ along the way, though …
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