Welcome to the forum and congrats on your new baby!
At two months of age, your bird is a very young baby and babies cry when they are alone from fear and anxiety - it's as simple as that. We accept this truth in human babies and even puppies and kittens but, maybe because baby birds are almost as big as adults, we seem to miss it in them. The reason why it likes to hide under your pony tail is that, most likely, it feels the same as being s under momma's wing which is the rightful place for a baby bird. So I am afraid that there is no advice that anybody can give you that it's going to change this. People will tell you to let it scream and not to go to it until it shuts up so as to 'teach' it that it needs to be alone but I am sure that the same people would not give this advice to a new mother who wants her baby to 'learn' not to cry when alone... I don't think that people do it out of meanness, mind you, I think they do it because, to them, a baby bird doesn't rate as high as a human baby or because they don't realize that the advice is cruel.
I don't know if you already know this, if you do, just skip over it but, in case you don't, let me tell you a bit about GCCs. They never do well in a cage alone and they never do well clipped - they all end up screaming and biting. Please understand that I am not criticizing you or trying to make you feel bad, I am simply stating a fact of nature. GCCs are intensely needy of human company (I often compare them to cockatoos in this) and, to them, seeing you and hearing you but not been able to reach you so they can be ON you (the only thing that makes them happy), is a kind of torture. I know this sounds extreme but it's the way nature created them and every single one out there that screams and/or bites because of a lack of enough or adequate interaction, is an unhappy bird because, to them, having their body touching yours all the time is not a luxury, it's a physical need. This is, of course, aggravated by the fact that we are talking about a baby. I have a female GCC right now but I've had four altogether (the others were rehabilitated, switched to a good, fresh food diet and rehomed -all came to me because of biting and, in one case, constant screaming and they all stopped and are still doing well in their new homes). My Cody is the sweetest little thing, she never screams, she never bites, she doesn't have a single stress bar (most GCCs out there have them), eats VERY well, bathes often, etc. She has a good size cage (but not huge) in front of a window and she comes out every day to spend a good two solid hours on me while I do my morning chores downstairs BUT she also has a mate so, when she goes back to her cage, she is not alone.
Are you handfeeding it? Because at its age, it still needs it along with soft food served fresh and warm twice a day. And, please, make sure you are not free-feeding protein food because that's real bad for them (they are mainly fruit eaters in the wild).