Aha, I see. Makes sense. 
I have not worked much with UV mapping so I simply thought the texture was it and it did not look as if anything was overlapping. See attached pic.

I will test making a "mane object" for each neck part, put hair on them and have them follow the animations. Should work right? :)

This is only part of the texture since one is not allowed to "redistribute" it. So this is not the UV map? If it is, could the pixels touching in some areas be considered overlapping?

Sorry for all the beginner questions. I do appreciate everyones input and guidance a lot. 😊