Me: ok brain gremlins, what kind of nonsense character did you invent this time?
Gremlins: we have made a queer who is extremely bigender but also a cis guy. These don't overlap but they're both true.
Me: how does that work?
Gremlins: *EIGHT PARAGRAPH WORLDBUILDING SALVO*
Me:
Me: ...huh. Alright, I'll accept it.
Gremlins: 👍🏽
Thinking about this motherfucker again so I want to share the "how" (more or less):
What if your job also assigned a gender?
To speedrun all the worldbuilding, the setting contains a Watcher of Stars who is basically a combination of oracle and political heavyweight whose entire duty is not just to do oracle bullshit but to do the oracle bullshit in service of preventing wars, disasters, infighting, large-scale problems, did I mention wars, the setting is absolutely rife with rich idiots with no braincells who would drive their kingdom off a cliff and the Watcher of Stars' job amounts to telling them "no" and then politically clamjamming them when they try it anyways.
The first Watcher of Stars did a bunch of fairytale stuff which effectively set the tone for all their successors, and among the many tones set is that the sitting Watcher is bigender. Not the person themself necessarily: it's that the Watcher of Stars (title) is bigender, so while you're acting in the role, part of your duties include being bigender. Expressions thereof are left up to the individual, but it's not any more optional than the oracular magic. (Anyone even the tiniest bit involved in the whole thing knows the deal so it's not getting sprung on anyone– by the time a successor actually gets picked they've been working towards it for years and have experimented with/planned their flavor of bigender fuckery.)
So the OC I was thinking of in particular was, before taking the title, a guy. During the working years s/he's bigender while doing Watcher stuff and a dude while he's not in garb/working (which works out to something like a 97/3 split in this case because *long eyeroll* workaholics don't get better when the commute home involves 30 minutes of shucking all those ceremonial accountrements). And after retiring... actually he knows what he's about and continues to present as bigender to people who aren't close, but friends/family get used to he/him pronouns. (I suppose technically the friends/family get used to using pronouns– the Watcher of Stars is such a lofty title you must always refer to them properly, no pronouns! (I am violating this rule because I'm the one making it up. Unlimited power, etc.))
And thus we arrive at a guy who is a dude but s/he's also extremely bigender. These don't overlap but both are true.
If you find anything here inspirational, I am very pleased and hope you run with it to dream up whatever floats your genderfuckery boat.