Bolin: sanguine/phlegmatic, Tahno: sanguine/choleric.
These two types are very compatible with each other, and Tahno probably has a few of them in his entourage already. (I think Shaozu is one, and the girl on his arm with the longer hair is very likely this too—the howl gives her away as sanguine, a melancholic secondary would make her too self-conscious for that, and a choleric secondary would make her sass Korra some in the restaurant.)
This, however, doesn’t mean every phlegmatic goes around giving their loyalty to every choleric they meet. That has to be earned, and in the restaurant, Bolin’s loyalty is given much more to Korra (and Mako, who isn’t present). Korra and Mako are antagonistic towards Tahno, so Bolin views him as an enemy instead of a leader.
Therefore, Bolin/Tahno becomes considerably more plausible if, a) Tahno becomes part of the Krew, and there isn’t a conflict of loyalty for Bolin, or b) Bolin is abandoned/isolated from the cholerics he’s loyal to.
Bolin would be very drawn to Tahno’s need and pain post-Amon, though if the above requirements had not been met, he would be conflicted about investing a lot in helping him, because he doesn’t want to “betray” Korra and Mako either. If convinced Tahno was worth the effort, he might try to bring Tahno into the group, and get Korra and Mako to accept him so he could help him in an above-the-board fashion. He might also just help on the side if he feels that Tahno is no longer a threat to/enemy of the group, and therefore it’s not a betrayal. He’s gotta do what he feels is right.
In most situations, sanguine/sanguine relationships are incredibly rewarding and fulfilling for both involved, and they love each other with abandon. But there’s a dark side to this here, because Tahno is terribly sad about something that (he believes) can’t be fixed, and sanguines don’t like things that consistently bring them down and make them feel bad. Tahno can’t escape those bad feelings, but Bolin can.
There’s a chance that Bolin’s sanguineness actually could make strides in cheering Tahno up in a way that he couldn’t cheer Korra up when Korra’s bending was taken. This would delight Bolin, because his phlegmatic side would feel all useful and helpful. But if his attempts failed, and Tahno stayed depressed….
Bolin would feel bad around Tahno too, and he’d get sick of feeling bad all the time. He’d feel terribly guilty for quitting on him, but honestly just want to avoid this sad sack of misery. (This same thing could lead to his fangirls abandoning him, and even possibly his teammates, if they felt his misery was impeding their recovery, or just weren’t as broken up about it as he was.) Sanguine + phlegmatic mixes love fixing problems, but they hate a problem that they fail to fix. Instead of making them more determined, they may start to resent the person they’re trying to save for making them feel bad all the time.
So how well that worked out would really depend both on how much Tahno responded to Bolin’s cheering up, and how patient Bolin could be.
As for the question of how open they’d be to a same-sex relationship, I’ve already said I think Tahno would be down with it. Bolin would probably have a hard time finding any problem with something that makes him feel as warm and fluffy as falling in love does, no matter who it was with. He’s a romantic at heart. If Tahno told him it was fine, that would also encourage him. He does care a lot what Mako thinks—not enough to repress himself, but enough to sneak around behind Mako’s back if he even suspects there’s a possibility of it causing problems—even if it turns out Mako would have been fine with it. This would irritate Tahno—he doesn’t like being shoved in someone else’s closet like they’re ashamed of him. He doesn’t understand why Bolin wouldn’t just tell people what he feels, because it’s easy for him to do.
I do suspect that Tahno can get competitive with other primary sanguines, just because he’s such a diva he has to be the prettiest princess in the land. Bolin has a well-developed phlegmatic side, though, and is pretty good at “just being over here…in silence,” which should appease Tahno. If Tahno can just be reasonable about this (which if Bolin helps him through the loss of his bending, I doubt he’d get worked up over something so trivial) there shouldn’t be much of a problem. The only way this could come between them is if Tahno became jealous of Bolin’s show-stealing antics with Pabu, and made a nasty comment about Pabu. (Can Tahno be this petty? Sadly, probably.) Bolin’s phlegmatic side will be incensed at an attack on the most defenseless member of his “family,” and that’s one of the few things he’s not going to back down on.
Bolin might actually make Tahno apologize to the beast, and then they’d have snuggles and do each other’s hair.
Their sex life should be pretty easy to guess from other posts with these characters. (By the way, when I say someone “bottoms,” whether in a het or gay relationship, I don’t mean that they’re the one being penetrated, or even the one physically beneath their partner, I mean that they’re emotionally following the lead of the other person, less likely to initiate, more likely to prefer that their partner is more active and makes more decisions. I don’t think humors have that much of an effect on how much you like things in your holes.) By that definition, and not the “he takes it in the butt every time” one, Bolin bottoms and he loves it. They are both very physically affectionate, though Bolin is likely to say things like, “I love you,” and Tahno is likely to say things like, “I know.” Tahno’s choleric secondary makes him just rough and edgy enough, but not to the point of being mean or precluding tenderness. Bolin really likes tenderness, and though he might not admit it, so does Tahno.
In short: if they can get over the previous baggage between them, and Bolin doesn’t quit on Tahno, Bolin could be exactly what Tahno needs in his life in a really hard time, and it would be a very rewarding experience for Bolin too. This is a relationship that would only get stronger once Tahno’s bending was returned, and they could go around being happy carefree sanguine people and getting makeovers.