Hi there,
Their eyes don't exactly change, they always have an iris.
I think it depends on the comfort and confidence levels.
My ringneck is 3 months old, almost 4, and I've had him for just a week.
I spent a lot of time with him and his pupils already started "changing". They will narrow their pupils when they're excited or happy as far as I know. When he sees that juice almond in my hand his eye starts to narrow, when he's eating it especially.
Unfortunately I don't have pictures, he doesn't like my phone too much.
Not sure if there's a specific way to trigger this, I think they just need to be comfortable! But I'm no expert!