Some headcanons that I think about a lot for Mute!Stan:
1. He didn't stop talking right away, it was a gradual process. Each year he spoke less, which got him into less trouble as a criminal, he had to do horrible things to himself to control his tongue and speak softly, he was yelled at a lot on the streets to shut up.
2. He learned some sign language on the street, but he wasn't fluent so he still had to speak sometimes.
3. When he got Ford's card he was barely speaking anymore, talking to his brother was one thing since his voice had been out of use for months already.
4. After Ford falls into the portal, Stan organizes his own funeral, his mother almost recognizes his voice because it was very different from Ford's at this point, so he decides to stop talking completely. People saw this as a response to the trauma of losing his brother so they didn't talk much about it.
5. Stan still opened the Mystery Shack, but without the guided tours. He simply made it more like a museum. He placed a speaker in front of each strange object where he recorded some descriptions of the creatures in advance, alone, at night.
6. He spread several speakers throughout the cabin with price information and random curiosities. As well as a larger speaker that constantly repeated that they did not accept refunds at the Mystery Shack.
7. The tours were created by Soos. As a child, he would visit the cabin with his grandmother and, since she was bad with the speakers, he would invent descriptions of the objects himself, which always gathered a small crowd around him who bought many more things on the way out. Stan hired him almost immediately.
8. Soos quickly learned sign language to talk to Stan and later taught Wendy, who also went to work there.
9. The kids learned sign language at home when they learned they were going to stay with their estranged great uncle who they had only heard about and who was apparently mute. It was a challenging project for them. Dipper learned it to challenge himself academically and Mabel learned it because it was fun to use a secret language and also because she thought it was like creating spells with her hands. They weren't very good, but they managed well.
10. When the portal is reactivated, Mabel is still left with the decision of whether to turn it off or not and for the first time in years Stan speaks and asks her not to turn it down, which shocks everyone because they thought Stan was mute since birth.
11. Ford is not happy when he comes back and Stan doesn't talk to him, despite all his knowledge of sign language it was never something that caught his attention and he suspects that Stan is just doing it just to be a jerk.
12. The kids get upset with Stan for being able to talk all that time and refuse to acknowledge his sign language for the rest of the day, avoiding looking at his hands the whole time, Stan panics and basically Soos is the only one who makes communication between Stan and the others viable because he translates everything Stan says.
13. The kids talk to Stan again the next day because he seems miserable for not being able to talk to them and also because they are so used to this type of communication that they forget that they were ignoring him.
14. Ford is the hardest to accommodate; when he's not deliberately ignoring Stan, he tries to catch him off guard so he'll talk. At one point, an argument starts at night on the porch, demanding that his brother talk, which leads Stan to try to talk again, but can't because he's desperate and has a panic attack.
15. During Weirdmageddon, they still switch identities, with Stan speaking and acting exactly like Ford. Bill is tricked because he knows that one of the twins can't talk and ends up being erased with Stan's mind.
16. When his memory is erased, Stan starts talking again. It takes a while for his voice to come back because he didn't use it much. The children still use sign language while talking to him to try to bring his memories back. The scrapbook works little by little.
17. With each passing day, Stan remembers a little more and each day he talks less until, by the time Stan and Ford get on their boat, he has all his memory restored and has stopped talking completely again.
18. Stan speaks few words sometimes, he says his brother's name, a few words of comfort or a greeting, only to Ford and in a low tone of voice, it doesn't happen much but whenever it does it brings Ford to tears, he preserves each of these moments as treasures.
That's it for now, I've been thinking a lot about Mute Stan in the last few days and I wanted to express these thoughts a little, whoever wants to add more things or take over the narrative from here on out, feel free, the floor is open.