Well, this is fascinating!
I've spent a good while lately on google and wikipedia and so on, trying to see if there was a term that fit me, and as far as I can tell/feel, none of the above does the trick so well as "niizh manidoowag" - the Ojibwe phrase that means something like "two-spirited".
I have a male body - and both a female and a male self, at the same time*. Neither of them have periods where they're dominant, they're just both running in parallel all the time. Androgyny doesn't seem to fit because it seems most people mean something more like "I am neither" with that word. Bigendered doesn't seem to fit because it seems most people mean something more like "I switch about between the two" with that word.
I'm reluctant to call myself niizh manidoowag or two-spirited because I'm reluctant to "spiritualise" something that's just my nature, and it's too easy to make something artificially extraordinary or spiritual, when it's just is how it is. So in the end, I'm experimenting with calling myself "ambigendered" which, with its connotation of "both at the same time" is the best I can do. Or in practice, what I tell people (when I tell people) is "I'm both at the same time" because if I say "ambigendered" I then have to say that anyway

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I'm new to this business in terms of terms - so it may be that there are already other words floating about that also fit my definition of ambigendered. If so, I'd be interested to hear them. It does seem like there's a whole swathe of not-quite-the-same-or-different terms because everyone's experience and identity is a little different from the next. I guess it never does any harm when using labels to add "by which I mean..." and not assume the next person means the same thing by it.