I was about to call my breeder on this topic!
My yorkie has the same thing. It's always there and then at times, it hardens up before I ever get to wiping it off so now there's a clump of hardended eyebooger on each eye and I tried almost everything to get it off.. I used soap, I tried slowly taking it off with a warm washcloth and it just won't go away! The only alternative I have is to trim it off with some scissors but I don't know if I should do that on his face.