Mango has two irises.His normal iris is blue so its like he has blue eyes but then he has a outer iris which is yellow so sometimes in pictures it looks like his eyes are yellow.I have seen videos of Plum heads talking and it looks like the outer yellow part kind of twitches.

Is it possible that what you're seeing is the third eyelid?

Third eyelid? I dont know what that is but the yellow part dosent exactly go around in a full circle and I saw a video of a plum head talking and the yellow part was blinking except not downwards like normal eyelids it was blinking from the side to the other side.

It sounds like the third eyelid aka the nictitating membrane. Birds have more built-in eye protection than humans do, and it does go from side to side. This link has information and pictures. http://10000birds.com/what-is-a-nictita ... mbrane.htm There are a other animals that have this too.

Are plum heads the only parrots that have this?

I think african greys might have it too, but I don't know. That might be something worth looking into.

I think all parrots have it.