Steps to reproduce:

1. Make sure "Hide Paper Doll" is disabled;
2. Spawn a parrot and tame it;
3. Make it go on your shoulder;
4. Sneak.

Expected results:
The parrot goes down with your shoulder as you sneak, and stay quiet there.

Observed results:
The parrot stays floating and freaks out, moving its head to all directions.

It looks normal in third person view, it's only bugged in the paper doll.