@erwil Mmhm good idea to study sign language. You could have your character do home sign if that character's world doesn't really have sign language or something. (Before 1500s, most deaf in the world used home sign or if there's few deafies in local, they use their own sign language)
Here are links to American Sign Language, ASL: aslpro and lifeprint . I’m not a HUGE fan of youtube videos because you don’t often know that person’s credibility. Lmk if your world is based on different part of the world because not all countries use same sign language. Good luck! And feel free to ask me any questions. I'm deaf but I am also selective mute (I have voice but I just don't like to use it)
Oh and check out Strays by Samantha Whitten- they have a mute character, Feral, who writes in different language that other character, Meela, doesn't know so they had to communicate through gestures, sometimes one word here and there in Meela's language. They wrote that mute character Feral very well! :3