Think back to the beginning, before the outbreak. Joel would probably be his truest self at that point. Even then he was socially disconnected. Sarah wants him to grab a birthday cake and he forgets. Later, certainly, he’s not socially comfortable. He ridicules Tommy for being a “joiner”. This is not a Heart Type.
He’s not a leader, either. That’s Tess. That’s Marlene and, we’re told by FEDRA, that’s Ellie. Joel is a follower. We can say, judging by the final episode, that he’s not a planner. When no one is in charge of him, he kills everyone in the building. He’s not strategic. (He would’ve kept the doctor alive if he had any sense of the post-apocalypse big picture.) We could even say that Sarah was the boss of him before she died. For Joel, he’s not just losing a daughter with Sarah (or with the threat to Ellie), he’s losing his purpose and identity.
This is a particular kind of Eight, the type society tries to keep busy in physical jobs. He’s a mastiff on a leash, if we’re lucky. In civilization, we want Joel to obey orders. In war, we let the dog slip.