I think you need to accept that most adult birds don't like to be petted. Baby parrots usually enjoy being cuddled and having their bodies touched (petted), but once weaned and fedged they usually don't, with occasional exceptions.
When you adopted her, did you envision having a bird that you could pet like a dog or a cat? If so, where did you get this idea, because it's not realistic.
She's already communicated to you that she doesn't want to be petted, and your efforts to change this may very well lead to her biting to get her message across and I'm sure you don't want that! Right now, she's let you know that she likes you and trusts you enough to seek out your company and snuggle up to you. Don't ruin that by pushing her.
At some point she may ask for and accept head scratches but they need to done when and how the bird wants them. If they'll want a scratch they will usually be in a very calm state to start with and bow their head forward exposing the back of the head and neck with feathers ruffled a bit. Then you slowly reach over the front of their head with your fingers bent, gently touch the back of the head or neck and draw you fingers forward using your fingertips and fingernails to gently loosen the feathers. When this is done when and how the bird wants its like birdie nirvana! They may only want it done for a few seconds maybe as long as a minute or two. If you don't do it "right" or if you hit a sensitive spot like a growing bloodfeather they let you know.
As far as disliking human hands goes, it's very common for even handraised parrots to decide they don't like hands. I don't know for sure why but I have a theory that some birds figure out pretty young that human hands can control and restrain them against their will so they decide to avoid them entirely. When I need to move my no-hands birds from one place to another or in and out of the cage, I use a stick perch. You could try wearing a long sleeved sweatshirt and pulling the sleeve cuffs over your hands so she can't see them. Sometimes that's all it takes.
Good luck with Phoebe! She sounds like a great bird.
Parrots move at their own pace. This is based on breed, individual personality, your personality and environment. They must trust you. Patience is the key. You honestly can't have enough of patience. Learn her body language and tells. This will decrease frustration on both sides. Knowing her tells will give you a good base. Give lots of verbal praise randomly and with the slightest desired behavior. Give verbal and a treats as you work with her. Even though it's training you want it enjoyable. Ignore undesired response. You want to avoid her using negative responses to train you to do what she wants. Yes it happens a lot. Be prepared for the testing of limits. My CAG loves to be held. Head scritches, cuddles are strictly on her terms. I know her tells. Unless something is necessary I give verbal praise and leave her alone. Go through the forums and online reading. Remember no matter what the speaker is saying or recommending it isn't written in stone. Use it as a basis.
thank you! That’s one of the things I haven’t worked on as much, learning her tells. I’ll keep at it with patience
