Is there a way to link a group of custom hair to a specific eyebrow recolor? Like, let's say I have a group of purple hairs linked together so the children will get random hairstyles within that group. Now, I want to link that group with purple eyebrow recolors. Is it possible, and if so, how do I do it?

I think someone were doing a binning system (that doesn't show as bin icons, but still kind of works) - as long as the "hairtone" number is the same in the PropertySet for the hairs and Texture Overlay/XTOL for the eyebrows, they should in theory be binned as the same color.

Brown is for instance "00000002-0000-0000-0000-000000000000", both for eyebrows and for hair.
A custom hair can look like this: "564bd0a2-431b-75f8-2790-a2be9d1aff65"
So picking a "random" bin for the custom hairs you'll use for all the hairs/eyebrows in one particular color, or using numbers by someone who has already binned theirs in this way should in theory work.

The hairs and brows will still show in the custom bin.

By using different strings you can filter even more, for instance by light/dark colors, or variations of color tones, at least if you don't want sims to show up with a very bright hair but dark eyebrows, or opposite, or two very different purple tones.

Make sure you use Hex numbers (to keep it simple, 0-9 and A-F).

Thanks! I'll see if that works.