Here’s a mini Gojou rant about what his S/O would be like, courtesy of @axymnn and I’s debate. Beware there’s manga spoilers below!!
Gojou is someone who’s complex. He’s seen as carefree and funny when with his students and trusted comrades, but he’s also serious and challenging with seniors and his enemies. We never know exactly what’s going on in his head, but we know for a fact he wants to guide the future generation so they can succeed him.
He’s someone who could only form a proper relationship with someone who he’s known for years. At least someone he met while he was still a student. To even consider a romantic relationship with someone they would have to have stuck with him through thick and thin. Gojou needs to know that if it came to him or the whole Jujutsu world, S/O would pick him a thousand times over. Even then Gojou will still keep them at an arms length, Getou was one of his trusted comrades and look how that turned out.
Gojou has had a target on his head the moment he was born. He has every right to be wary of any potential lovers. If a random person waltzed in and suddenly attempted to become friends with you, you’d be nervous. Any targeted person would.
Gojou’s S/O would have to be self-sufficient in sorcery, and when it comes down to battling Gojou shouldnt have to worry about them. If they weren’t powerful enough, Gojou wouldn’t pursue anything further than a friendship. Gojou is confident in his abilities, but he can’t always babysit S/O. They’d be a perfect captive to use against him. 
Let’s say in this situation Gojou does pursue a relationship with S/O, he isn’t emotionally available. He can be a downright asshole sometimes, so it would be hard to have a heart to heart with him. He may take S/O out and give them the occasional kiss, but he is not someone to go for for words of affirmation. Gojou has seen his fair share of death, so he’s most likely terrified of confirming anything. The second he says ‘I love you’ he’s afraid they’ll leave him, or even worse betray him.
