Kogane's obsession over his brothers Seikin and Kyou made it difficult for him to fall in love with someone else and this issue is compounded by his brothers being protective of the youngest sibling, Seikin moreso than Kyou. Even if the youngest brother were to have a different mindset, it isn’t easy to bond with someone when he rarely meets people offline. Even on the times where he is offline like say during dance, capoeira or fencing classes, he is quite standoffish with little to nothing to say. He does have tons of friends online but doesn’t really bother meeting them at all.
So, the only times I can imagine Kogane even starting to have the notion of bonding with someone else is when Seikin and/or Kyou is/are taken. Or an AU where Kogane’s upbringing and the relationship between the three siblings are different. Or main verse but they met when the three of the siblings are doing a band gig (he stands in for Kyou as a fellow twin though mostly for the parts Kyou and Seikin can’t do, in other words mostly dancing, screaming, growling and rapping). Seikin, if taken, might even make the effort to push Kogane away from him and onto someone else.
Speaking of 'Seikin if taken', Seikin's partner is also a factor of how willing he is to find a partner since the older brother's situation changing affects the twins as well. Even more so if Kyou has something in mind at the same time too. For example...
With @gloryundimmed's Kai (a deviation of the main verse where the siblings decide to take over a family branch as la ma.fia), Seikin and the twins took over a branch family their uncle once led and the three siblings rule as a triumvirate. Kogane wouldn't really bother looking for a partner in this when he still has Kyou and the triumvirate. If anything, he might follow his parents' footsteps and take up an arranged marriage. Unlike his older brother and his twin, Kogane has no qualms dirtying his hands over a job the branch family needs done and is the branch's family go-to.
With @hellbloom's Loux, Seikin was given the offer of immortality. Kogane still has Kyou but honestly... the twins had a falling out over the topic of immortality and the older twin Kyou decided to take Kogane's spot of next in line as patriarch instead. With how Seikin and Loux acts, the youngest brother felt like he was forgotten and that feeling lingered more than he would like to admit. Enter Pheo, they somehow got together, much to Seikin's surprise. Cause Seikin genuinely did not expect his younger brother on his own accord to find a guy like that.
With @soulcarved's Eito, Kogane is still pretty much the same guy as he was before. But much more of a busybody, he'd be in Seikin and Eito's way when he can (Eito, you gotta be less scared of him or you are not gonna get away from him). Going so far as to spent time with Eito's twin Aika in order to dig up dirt that he would not have gotten otherwise while genuinely wanting to spend time with her. Though since Eito is Seikin's type, the older brother took much more effort to hide himself and his boyfriend, leading to Kogane spending more time with Kyou and Aika instead.
With @kisumitenderly's Kisumi, Kogane absolutely could not stand this guy. Not only is this pink haired guy NOT Seikin's type at all, this guy could not tell him and Kyou apart. Yeah sure, identical twins but seriously? Seikin did not help either and Kyou decided to pursue music full force. This left the younger brother alone to doubt his self-worth. Giving up Seikin took a lot outta him, so he decided to game with Hayato as much as possible only for Kogane's dumb ass to have a crush on him. It's not like he wanted to have that crush but since he has it, he's gonna try his damnest.
I try not to make Kogane an incel goober but since Seikin is just that perfect flashy yaoi hands snazzy golden blond guy and Kogane really is the opposite of Seikin and tends to be in the older brother's shadow. Someone gotta convince Ko that he is his own being and that he needs to use his own words and act too instead of letting Seikin do all the talking and doing tbh. Beneath the surface, Kogane is not just some dirty blond boring kid but someone who can be fiercely loyal, still a bit awkward yet lovable kind of dude. Just remind him that his older brother isn't everything there is in this world.