I allow Charlie on my shoulder, and he often flies to my head before climbing down to my shoulders... but he's not really a shoulder bird. He prefers being on my hands or arms and sometimes in my lap. Don't really know why. Having said that, he does have an issue with me trying to blow my nose with tissue or at times running water - especially if it's fast running water. If it's slow running water, there's no issue. Easy to avoid situations where he would get upset.
Casey often flies to my head, shoulders, arms, hands, chest, butt.... really, any place she can land!!! Doesn't bother me in the least!
Tomi Girl isn't really tame but she's not wild, either... she has been on my shoulder before but she prefers being around, on or in her cage.
Jayde I've had on my shoulder before I even trusted her! And yup, she bit me, too! She's not hard to get off of my shoulder, even if she doesn't step up from my shoulder, and her biting/nipping is really to a minimal now anyway so I do trust her to be on my shoulder now. I think allowing her onto my shoulder helped her to really come out of her shell and learn to trust me.... saying that, I *WOULD NOT* recommend anyone else to do as I did! I took that risk because she took the risk that I wasn't half bad and climbed to my shoulder. The first physical interaction (besides scritches and kisses) that she initiated in over 6 months! (her foster mum had her for 6 months, and Jayde would not leave her cage! I have no clue before that!)