I mean...choosing to dress yourself in a specific way is still a behavior. ^^; And considering how closely clothing is tied to gender expression (and has been for centuries), I feel like separating the two is kinda splitting hairs...?
But that's more of a nitpick; I think this is the real crux of the issue:
I understand that choice for a definition. But as other people have stated, most people don't share it, so its usefulness is clearly limited. :T And secondly...I think a lot of people, when thinking of a woman breaking free from the gendered expectations placed on them by society*, would rather not immediately place their behavior under another gendered label.
I believe this is the reason why 'tomboy' is becoming outdated-- it comes from an era where there were only two options; girl or boy. So a girl who does not act like a typical girl must instead be labeled some form of boy...rather than just a different kind of girl, or god forbid, just a human being who isn't necessarily expressing their gender through every action they take.
Like, we're at a point where the idea that all humans should be allowed to experience toughness and softness, to be assertive or cooperative, to be loud or quiet...is slowly becoming socially acceptable, at long last. So a word that calls a girl with a certain personality type a "___boy" is slowly becoming unnecessary.
And when I say slowly, I do mean slowly. Of course it's not like that everywhere, or for everyone...I grew up using 'tomboy' too, and uselessly trying to figure out whether or not it applied to me (#nonbinary). But I...don't see a need for it anymore. And I'm not surprised that other people feel the same, in a forum full of writers and artists. ^^; I.E. people who tend to think a little more deeply about social norms and the way words shape our thoughts.
*You mentioned a lot about how this 'tomboy' is technically immortal, and so her behavior can be considered particularly masculine relative to the time period she actually came from. And although I think that's valid, I feel like there could be a better way to express that through her design.
I know your emphasis is on her personality (word choice and mannerisms too, I hope) but...frankly, the idea that an immortal woman who clearly has a unique relationship with gender just looks like a 'librarian' (like, a design that could read as 'ordinary woman' across 300 years of fashion, if not more) is really disappointing, ngl.
Why not have her wear antiquated mens' fashion that reads as more feminine today, displaying her supernatural age AND her 'tomboyish' personality simultaneously? Or go the artsy route and design something original that reflects her attitude; lots of big showy clothing with striking colors to communicate her dominant attitude.
Even just changing the pose in that artwork could help: why is she just calmly waving? If she has such a blatantly 'mannish' personality, show it-- cross her arms, let her stand with her legs apart, have her look directly at the viewer instead of vaguely off to the side.
Like, sometimes when people don't understand what you're doing with a character, it's because you're not giving them information that actually conveys it. And I feel like that's the case here...I don't think it would be impossible to have that character read as a 'tomboy'. But I don't really see anything that would convince me to read her that way.