hello! Welcome to the forum! What's your GCC name?? GCC are such awesome burds! Mine is named Ta-dah.
So sounds like feels safe in cage, likes you wants a relationship. But out of the cage is feeling overwhelmed and fearful. If I had to guess I say has been spending to much time in the cage , and tgrn maybe you have reached in and forced out.
This can all be overcome. I would put a perch on the door if it is a swing open type, as well as one on the outside next to the door. Also set up the top outside with lots of perches, something to shred, mine love yucca chips. Put a food sbd water and treat dish up there as well. It can be helpful at first to put a small treat dish on the outside of door next to perch.
Take a couple of hours when you don't need to rush. Make sure ceiling fans are off, doors to otger rooms are shut, any other pets locked up. Get you a comfy chair, set it sideways and about 3- 4 feet from cage. Have your snacks drinks and what not. Open the door show him the treat ( safflower seeds work great) out it into the treat dish next to the door. Then go sit in your chair. You can talk calm to him but don't focus on him .
Hopefully he will come out and get the treat. When he does tell him how good he is. Hopefully he climb up and explore stuff on top next. When he seems calm snd comfortable uo there. You will say hi, show him the treat and go out in the dish on top. Then sit back fine. Praise him when he takes it and chat and encourage him. Every do often go out another treat in dish. Just let him hang out. Let him build his confidence and explore. If he is good about taking treats by hand then just say hi come here and give treat. Then go sit back fuen. Repeat lots. When ready fir him to go back to cage. Have a slice if apple, a millet spray, a grape or something wonderful. Make big deal of showing it to him and out in cage and tell him time go go back . Stand back away from door. Every step he takes to door praise bunches. When he goes in tell him how good he is. This may take time, especially the first few times you do this. Be patient. I've have taught non tame budgies, and fearful bee burds to go back to cage with just a few repetition.
Then take a few days to keep repeating. He will soon find that with no pressure, and lots if treats, that coming out and hanging out is fun and not scary. When he us confident wuth thst , I would start working on target training on top of the cage, and step up sbd back to cage, giving kiss, ect. Remember very shirt less than 5 min training sessions, with 5 ir less repetition works best with parrots. Then wait 20-30 min and repeat. They can get bored quick, and sometimes after they have masters something they font want to do it over and over like a dog would. Shiw sbd teach easy forage stuff for a treat to. Like show treat sbd cover with a little square of paper. Burd tricks on YouTube has some food target training videos snd teaching foraging videos
Hope thst gives you a good place to start.
And yes pay attention to body language, they giving you sign before the bite, you don't want to push them to bites. My GCC can go from things are great, to im trying to kill her she must bite me i pay attention, I don't get bit, a few seconds later no big deal she is over it, and we are back to being fine. Green cheeks do not back down, and they have a strong sense of what is right and wrong. If they feel you did wrong they let you know. But they are sweet and want us to be good humans, and will forgive and forget, if you say sorry and stop what you were doing wrong. Its very easy for them to get fearful of hands . I've hadvmibe fir 7 years and I still will walk over sbd give treats by hand several times a day.
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