Hmmm... I am trying to figure out how to correctly answer your question because, although it sounds easy enough, it's not - and I'll tell you why. When choosing the right species, one has to take into consideration many things: species (companion or aviary, pair or flock-oriented, small, medium or large, etc), gender (and which gender is the dominant one in the companion species we choose), infrastructure (room enough for an adequate cage, ability to bird-proof, etc) and, most importantly, the degree to which each person is able and willing to provide what the bird needs.
Now, the greatest majority of people asked would say they want a sweet-tempered companion parrot that can learn to talk and is real pretty (you would be surprised how many people choose their parrots going only by the way they look!). But the problem with this is that not all parrots learn to talk (only 10%) and that most people cannot give a companion parrot the kind of attention it needs (who can spend 24 hours a day, 7 days a week, 365 days a year with a bird for the next 30 years? Nobody, that's who!) and that their beauty might not last (pluckers!).
Everybody (and I do mean EVERYBODY with absolutely NO exceptions) has the best of intentions and EVERYBODY starts off real well - they spend a lot of time with them, they cuddle them, they feed them right, buy them all kinds of toys, etc. But, as time goes by, what was a super novelty and a source of intense pride and joy becomes commonplace -and this is no criticism about anybody in particular because it happens to all of us - it's human nature and we can't help it. And the bird that not only NEEDS the constant company and attention to feel safe and content (not their fault, it's the way they are made - one could call it 'parrot nature' and, like us, they cannot help it either) and who was getting it at the beginning is no longer getting what it needs. The neglected bird becomes despondent and very resentful of the human who after establishing a bond with it, no longer 'performs' what the bird considers their 'duty' and retaliates by screaming, biting, etc. (I have this argument with my husband all the time because he does not spend as much time as he should with his parrot so, every now and then, she bites him - and he deserves it!). This is the reason why your brother's GCC bites. Namely, it is not getting what it needs and it rightfully blames the humans for it (parrots are VERY intelligent -they add 2 + 2 and get 4- and they know very well that it is our fault). The thing is that this despondency and aggression is not limited to certain species, it would be the same with any parrot that is neglected. There is no species of parrot that would become used to being neglected. It doesn't happen. Some of them resign themselves to the chronic depression and anxiety they live with and slowly deteriorate both emotionally and physically, some of them become aggressive and start biting, some scream constantly in their despair and some become so depressed and heartbroken that they start pulling their feathers and even self-mutilating. Now, for most people, the best species are aviary ones kept in bonded pairs as all they need from us is good care/husbandry because they get their emotional needs met by their mates. But, they are not companion species and, unfortunately for the poor birds, people want what they want and they want companion species.
So, in reply to your question and paraphrasing it so it gives a more accurate description of what it really entails: is there a species of companion parrot that upon being neglected will remain happy and healthy? No, there isn't. Cockatiels need company and attention, too but, as you noted, they don't bite very hard and this is not only because they have small beaks but because they are, in my personal opinion and experience, the sweetest-tempered of all the parrot species (GCCs being second).
In my personal opinion, the best thing for you and your bird would be for you to adopt another tiel, preferably of the opposite gender and tame both of them correctly (and I say 'correctly' because a lot of people take advantage of the good nature of tiels and use flooding techniques with them but that is not recommended by anybody who knows anything about parrots and training them). They will not give you the deep bond and, most likely, the male won't learn to talk but he can learn to whistle different songs and they can both like/trust/love you as another member of their flock.
Another thing you can do is talk to your brother and see if he would be willing to 'share' or give you his GCC. He is, obviously, not paying enough attention to it and the bird is suffering for it so it would be the kind thing to do (offer to do all the work, like cleaning the cage, preparing its food, etc). If he does and you spend a lot of time with the bird every single day, it will stop biting and will love you to pieces (my most affectionate bird BY FAR is Codee GCC - she never, ever bites and all she wants to do in life is perch on my shoulder, cuddle next to my neck and kiss me over and over and over and over -I call her my 'kissing fool'
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