You might have noticed that this model's eyes don't quite react to light the same way others do, as they usually appear flat white, even in shadows.
https://imgur.com/a/dLIVgcx

Hucket helped me fix it for a project, and I figured I'd pass along the knowledge of how to do so. Don't worry, it's a relatively simple fix. Mostly everything here can be done with Override Materials, but I'm going to focus on how to fix the .VTF and .VMT files so you don't have to do this every time you use the model.

NOTE: You will need VTFEdit.

Firstly, find the material files in:You're looking for eye_l.vmt and eye_r.vmt. Everything you do must be done to both of these files- their contents should be identical. I suggest you pick one to make changes to, then copy/paste the contents to the other one when you're done.

Open the file, look for the line for "$AmbientOcclColor", and set the parameters to 0.33 0.33 0.33. That's the reason the white appears so harsh- because it's quite literally maxed out.

But oh, no! Her eyes are now missing textures! That's because they lack an $AmbientOcclTexture, which are basically colorable pre-rendered shadows.
https://imgur.com/a/4xk8lZv

Thankfully, because the eyes use the EyeRefract shader, they are standardized, so you can simply copy any .VTF file from any Valve model or community model that follows Valve standards.

I originally used Fiki's Improved Scout's, which is eye_extra.vtf, before deciding that for my use it looked better completely transparent. Use whatever name and texture you want as long as the naming scheme is consistent, but this guide will assume you've done the exact same.
(If you need to find a model's $AmbientOcclTexture texture, find the .VMT files for its eyes and look for the attribute there. If you can't find it, it may not have one.)

Once you have your new file, go back to your eye_(l/r).vmt file and add the following line somewhere: I guess texture stuff is typically towards the top, but to my knowledge it doesn't matter.

By the end, you should have something like this. Remember to apply all changes to BOTH files! If something goes wrong, you can just copy/paste it.
https://pastebin.com/zyNiCsK1

And there you have it! Her eyes are no longer permanently bright white.
https://imgur.com/a/DvlRAZ5

Huge thank you again to Hucket Bat for helping me figure this out.