Im aware this is an old topic but I recently downloaded these models and I know someone will probably need this eventually

with that out of the way you are going to need a few things first:

1. VTFedit
2. A painting program (I used Krita out of preference, but anything with layer functions and a blending brush is fine)
3. A rip of the Splatoon 2 Callie model (I got it from https://www.models-resource.com/nintendo_switch/splatoon2)

The reason you need the Callie model is because of the texture PNGs which will be used to replace the VTF file for the eyelids. Now to do the actual fixing:

Open up your workshop folder and find the folder squid_sisters (if you are having trouble finding it the path is C:\Program Files (x86)\Steam\steamapps\common\SourceFilmmaker\game\workshop\materials\models\props_splatoon\squid_sisters).

Once you open it, find the VTF titled "callie_eyelid" do not confuse this with the VMT file since they are named the same, you can distinguish the two by the file size (the VMT is usually 1 or 2 KB while the VTFs are much larger) you should drag this file out and put it on your desktop or something for easy access

Now extract and open the Splatoon 2 Callie model and find the closed-eye texture titled "m_eyelid_alb.3" and put that next to your VTF wherever you put it.

Next, open up the VTF using VTFedit and in the top left corner click "File" and click "Import", then select the eye texture you just extracted and hit open, do not mess with the settings on the import screen and just hit "OK", then hit "Save as" and save it as "callie_eyelid" it will tell you there is another file with the same name and will ask if you want to replace it, click yes.

Now open up SFM and load the model to check how it looks, you will find that the eye texture doesn't look quite right (something like this https://imgur.com/ftWETRP) this is where the painting comes in, before you close SFM take a screenshot to use as a reference and try to get the skin tone to match as close as possible, it will be pretty much trial and error and constantly checking the model before you get it right

I got mine relatively close to what it should be (https://imgur.com/a/8gZgGLb) if you look closely, you can still see the lines a little bit but it shouldn't be much of an issue. if you render a poster and it is noticeable I recommend post editing to try and fix it it instead of going back and trying to screw with the models texture more than necessary

This most likely isn't ideal, but I've found no other way to fix it, I have redownloaded and verified my cache but that did not do much. I am willing to post a download link to the "fixed" VTF I worked on for you to use without doing it yourself if you ask me for it

I hope this helps :3

EDIT: I'm not sure why my imgur links are being blocked as malicious but oh well, sorry about that >.>