He’s an orphan. As far as he knows, his father is a deadbeat dad (whatever the romantic stories his mom spins) and his mother dies while he’s young. It isn’t until the second Guardians that Quill comes to see Yondu as a father figure. Much of Quill’s character is defined by this. He wants a family, and he’s very forgiving of someone like Rocket, who’s so hard-shelled he can be impossible to know.
I do think that his openness to life, regardless of his childhood loss, is part of his Enneagram. Different numbers would react differently to being an orphan. He’s still so willing to engage and believe in people. When he gets to Ego, he believes a little too much and too easily.
So I want to say Heart Type. His inability to form a plan is a running joke in the Avengers. (Not a Head Type.) He’s physically competent, but it doesn’t define him. (Not a Body Type.) He’s no Three; his luck is too haphazard. And he’s not acerbic enough to be a Four.
Two. He collects songs, of course.