We recently rescued a GCC that had spent a lot of time caged in a garage and he exhibits this very same behavior constantly. He's definitely a mixed bag, and its hard to tell how long it will take to break through his shell. He's very cage protective, ruffled up and neck swaying when we get close or open the doors, but ignore him for even a few seconds and he squats down, tilts his head up, and starts mini-flapping his wings at us and chirping. Whip out a sunflower seed and present it to him and instantly he changes to happy bird, coming to the cage door or even out of the cage on top of the door when it is open.
He's on a diet of Harrison's and Rowdybush mix, with some Zupreem uncolored mixed in, as he likes the big pieces now and then. He also gets a bowl of fresh food each evening, but he tends to ignore anything other than apple pieces. I've tried a chop mix, but he's definitely got a sweet tooth and only picks out the apples.
I don't think his behavior is hunger related, so I'm inclined to believe he wants attention. I think deep down he really wants to be with us, and he displays the desire to be close to me when I'm near the cage and he's outside on the top of the door, but he just can't break the touch barrier. Since I have no real information about his previous home(s) I don't know if he experienced anything that might cause distrust, but I can only hope that the slow approach will eventually win his love. He's started accepting seed treats from the back of my fist, so I think that is a step at least. Last night he went nuts licking at my extended arm, but he wouldn't step forward. Baby steps for now, but we hold out hope.
Just something I wanted to add, since the behavior in the original post matched exactly what we are seeing, and had no idea what to make of it.