This is what I do.
Believe me Im not groomer
..........I cut the hair directly under the tear duct down the sides of the nose and all the way around the eye very short with mustache scissors.
You wouldnt beleive how much it helps. If there is some drainage, well it wipes clean much easier with shorter hair. And there is alot less build up. Yorkies are sure prone to eye irritations.
If the drainage is excessive your yorkie may have an eye infection. If you note green or yellow drainage it isnt normal. See your vet for possible treatment.