Character would need to be expressive in other ways that I feel like most writers fail to capitalize on (properly). I am trying to think of mute characters in media that are written well and the only one that comes to mind is Christine Royce from Fallout New Vegas. Other than that I am drawing blanks personally.

That said I think this might also fall a bit into the 'stupid people can't write smart characters' thing where it's really hard to express (faithfully) something that you're not yourself, which isn't to say 'you shouldn't do it' but it probably does mean you're going to give a fairly non-faithful rendition of what it's like. Stupid people don't know how it feels to be smart, and therefore they project what they believe a smart person is like onto the character.

The same is true in reverse; smart people don't really know how dumb people operate so you see most renditions, written or otherwise, devolve into hurr big caveman strong smash. That's not faithfully how dumb people are, to put it bluntly.

I would be wary of falling into that pit when you are writing a (selectively) mute character. Maybe if possible I'd find some sort of resources on (selective) mutism from the POV of the person who is (selectively) mute. I would guesstimate that the experience of a mute person probably isn't as 'simple' as others might want to dumb it down to - and a lot more goes into it that we probably aren't anticipating because we don't live life like that.