I've only tested this on 1.12.1, but if you get parrots on your shoulders, when you walk they still do the walking animation.

To replicate:

1) Tame some parrots.
2) Get them on your player's shoulders.
3) Press F3 until you see your face.
4) Walk around, and watch the parrot's feet. (If they are considered sitting on your shoulder, they shouldn't be walking on it...)

Edit: In the pictures below the parrots feet are in different positions. (They are the only gray on my friend's shoulders.)