Tahno: sanguine/choleric, Mako: phlegmatic/choleric.
Both being choleric secondaries, and meeting as rivals, their first instinct is one of mutual dislike. Additionally, since Mako is phlegmatic, he’s very defensive of his in-group, and would do anything to protect them. If he perceives Tahno as a threat to the people he protects in any way, he’s capable of being downright cruel to him.
But phlegmatics are also those need-seeking missiles, and Tahno post-Amon might be a horse of a different color. Phlegmatics don’t like injustice or suffering, and he might be moved to offer help, if he was convinced Tahno was in genuine distress and no longer a threat to anyone. If Tahno wormed his way into Mako’s heart, he could find himself on the nicer end of Mako’s fierce protection of his loved ones.
Tahno definitely loves him some primary phlegmatics, but he probably avoids phlegmatic/cholerics, both because he’s vain and insecure and doesn’t like to be challenged from within his own group, and because he finds them a bit boring. Phlegmatic/cholerics can be rather conventional, interested in “normal” things, while sanguine/cholerics like to rebel a bit. Tahno would see Mako as kind of a stick-in-the-mud, and rude besides. He’s used to being unquestioningly adored, and he can be forced to respect undeniable authority like Korra’s, but he’s not going to sit back and take sass from some phlegmatic.
Even if they did move past that, forex if Mako helped him when he was hurting from the loss of his bending, and he came to like being protected by Mama Mako, there’s still the fact that Tahno might find Mako a bit cold for his liking. Tahno’s humors are hot/hot, and Mako’s are cold/hot, so while there’s some flashes of passion in there, he’s just not as demonstrative with his affections as Tahno would like. Mako’s humors make him more reserved, and Tahno’s the opposite of that, he needs a lot of attention to be sure that everyone still loves him or he starts to freak out.
If Tahno took out his frustrations on Mako, there’s a danger Mako would handle it with his primary. If he handled it with his secondary, they’d have a big dramatic fight, and Tahno likes drama and attention so that’d make him feel better (though it would exhaust Mako), but if Mako responded with his phlegmatic side, acting passive, withdrawn, and appeasing, Tahno would only feel shut down and ignored, and get more butthurt about the whole thing.
Then there’s the fact that they’re both men. While we never see homophobia in the Avatarverse, it’s because we never see queer people at all, which in some ways is worse. They’re entirely invisible. I’ve come to the conclusion that when queerness is invisible in a fantasy world, that’s not “neutral,” it’s not inconclusive, it doesn’t mean that they could just be fine with it. It means homophobia is alive and well, because queer people exist, and it takes a lot of pressure to make it seem like they don’t.
Of course I’m assuming for the sake of argument that both of them have a sexuality that would be open to dating men, since it’s obviously a dealbreaker if Mako is 100% straight. (Tahno is always bi in my headcanon anyway.) I think Tahno would be quite willing to embrace this side of himself, because sanguine/cholerics are rebels, and if something’s socially taboo that just makes it a bit more exciting, doesn’t it? Dating a man would be scandalous and attention-getting, and he’s all about that. He’d probably do it even if he was straight, just because he thought it was cool.
Mako, on the other hand, probably hasn’t even given any thought to the possibility that he might be attracted to men, whether he is or not. He tends to be very conventional, and he just sort of learned that men like women, so that’s what he does. Because of his choleric side, he might even get angry at the insinuation that he’s gay, or angry at another man for “making” him feel gay. He could definitely feel threatened by Tahno, since Tahno’s choleric side is attractive to Mako’s phlegmatic primary, and his sanguine side is just attractive to everyone. He doesn’t necessarily WANT to consider that he may really like that sort of thing.
Sexually, Mako is a bit more prone to bottoming, but he can also give as good as he gets when the mood strikes him. Tahno will definitely be the one pushing the envelope more in the bedroom, doing things Mako never would have thought of, but since his sanguine side generally leans towards hedonism, it’s not something Mako will necessarily mind.
It’s not the easiest or most stable relationship, but if Tahno doesn’t get bored, and Mako can be a bit open-minded, it could definitely work.