When a parrot is tamed and then the player changes to spectator mode, the parrot will still go to player's shoulder, and turns invisible when does so.
When a parrot is tamed and then the player changes to spectator mode, the parrot will still go to player's shoulder, and turns invisible when does so.
Tested and can confirm this to be the case.
When in spectator made if a parrot was flying to you when switching mode it will land on your player also if you fly over a parrot while in spectator mode it will also go to the players shoulder, in both cases it will turn invisible.
Video deminastrating the issue.
https://gfycat.com/RespectfulBitesizedAlbacoretuna