Quick question. Cheerio doesn’t mind stepping up or sitting on my shoulder, but when my hand approaches his head (head scratch) or back, he runs away. I think it might have been possible that he was traumatized. Is there ever gaining trust once it has been semi broken? I feel bad that he has fear in the back of his mind. Or maybe he isn’t scared at all but he just doesn’t want to be petted anymore? It’s weird.

Side note: he likes beak rubs, but I have to be cautious so that I don’t seem threatening.

Try to offer him food out of your hand.

Then when he's used to that bring your other hand closer and closer to him while he's eating, but keep it still.

If he's used to that, you can start moving your fingers a bit (say when you're holding your wrist and he's eating out of your palm)

If he ignores your moving fingers you might want to rub him once and see how he reacts to it...

It' going to be a long journey, but gradually move up this plan on his pace. It should work.

Yes, food in the hand is the way to go. Or having him take something else out of your hand that he likes, like a small toy.

Do lovebirds like to have their heads scratched? Not all parrots do. For example princess parrots don't preen each other on the head, so they don't really appreciate when humans try to do it.

Even with a species that likes head scritches in general, some individuals don't like it. Or they may run away because they don't understand what you're trying to do. Some birds that are hand-shy will let you rub their head with your nose, which is weird because a head is a lot bigger than a hand and it seems like it ought to be scarier. If a bird will let you rub its head with your nose, you can often sneak your finger in without the bird noticing at first, and it will eventually learn that finger-scritches are good.