You want a tatooist to give you permenent eyeliner? no way
firstly, they (probobly) arnt used to applying makeup, so you could go in and describe it to them and come out looking like a racoon
secondly, I dont think they would have the right tools, I think permenent eyeliner is similar to a tatoo but not the exact same.
thirdly, you want someone with no expeirience in doing it to put a big needle near your eyes? You would be the tester for that person.
and because of all these reasons I doubt you can walk into a tatoo parlor and get it done, they probobly dont offer it. Why not go to the beauty clinic? Seems like commen sense to me.