I know what the problem is. It will take some time and many pictures to fully explain for the general public, but perhaps in the meantime you can make progress with a quick explanation here.

Your specular map is giving bad data to the shader. The specular map is supposed to represent how shiny the surface at each point. When you have a surface that is supposed to be modeled as a single material with uniform characteristics, you don't really need a specular map.

But - skin is shiny, mascara is not. Any form of powderized makeup is less shiny than skin, and mascara is particularly designed to be matte. Yet your specular map is uniformly gray on the eyelid. The lightening you see is simply a result of that information - the whole eyelid is shiny like skin.

You should draw the mascara onto the specular map in black. And the eye shadow should be drawn much darker than the skin parts on the spec map. Your spec map is slightly darker on the eyelids, so the lids are somewhat less shiny than, for example, the forehead, but not by much, and it is still uniform.

The spec map must indicate the shine level accurately. Until you do that, it will present the wrong amount of specular. You have four different real-world materials on the face and your spec map doesn't capture that at all. The four materials are skin, eye shadow, mascara, and lipstick/gloss.

You have an even more unusual incorrect spec map on the lip area. There is a highlight drawn on the lip. This produces a very strange specular effect. The lips should be uniformly more shiny than the skin, if your intent is that they lips look like lipstick/gloss or wet lips. Dry lips should be the same specularity as normal skin.

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