The title says it all: I'm wondering how the eyedropper actually works. Is it reading the instructions the graphics card sends to the screen?
No, it reads from the file, not the screen image.
The distinction is important, because you need the numbers in the actual document, in the actual color space of the document (sRGB, Adobe RGB, ProPhoto etc).
The numbers sent to screen are different numbers. They have already been converted into your monitor profile, and the numbers remapped to display correctly in monitor color space, which is different from the document color space. This is standard color management that Photoshop does on the fly.
Where you can get confusing readouts is if you work with untagged images. Never do that! The file should always have an embedded color profile.
Thanks. Does its operation change when you move out of your document (say, onto your desktop) to sample something?
That's actually a good question. I don't know. Maybe someone else knows -
It seems when one leaves the canvas and picks a Color from the Finder area with the Eyedropper Tool the RGB values are not converted to the active document’s Color Space. (Instead they seem to be identical to what one would pick in a screenshot of the Finder area.)
Same for when one drags over to another image with another RGB Color Space.
So it switches to "screenshot mode". It makes sense and is probably the only workable way.
Any chance you could explain what it is actually doing? I use it all the time, I'm attempting to get my head around how it finds the numbers that it reports.