In my exploration based 5e game the group are about to enter an area where the local population (known as Forestfolk) communicate largely through sign language. I want to roleplay this effectively while remaining respectful of real languages and real people who rely on sign language every day.
A bit of worldbuilding lore
Originally the Forestfolk used sign language because one of the native races is commonly deaf and the others learned it to accommodate. They soon discovered it grants a distinct advantage to moving silently while hunting, communicating at distance, communicating across dialects or distinctly different vocal anatomy and at allowing a better connection with nature by not disturbing it with harsh noises.
Eventually it became the cultural norm to communicate almost entirely in sign language. Spoken word reserved for when something significant or ceremonial needed to be said and even then they both speak and sign the words.
Learning to sign and understanding the reasons for it will be part of earning the trust of this faction and something I want my players to feel natural, realistic and fulfilling.
What I'm looking for
I (to my regret) do not know sign language. However I'm consistently committed to my homebrew worlds being diverse and representing the full spectrum of (meta-)humanity, which should include those with disabilities. It's important to me to portray these respectfully but also make the use of sign language meaningful at the table.
By meaningful at the table I mean that I don't want to simplify it to "they say X in sign language" as I would with Elven or other fictional language that I also don't know. However I'm having trouble figuring out how to do that. I don't just want to wave my hands in the air while talking as I think that would be demeaning.
So far my best plan of action is to try to learn a few meaningful gestures or phrases and use these regularly so that players can learn their meaning through repeated observation. But I would love some advice from people who can actually use sign language on the best way to go about it, in particular those that have implement it at their table with other players who don't speak it.
Answerers are reminded of Good Subjective / Bad Subjective, I'm looking for first hand experience or well supported research not idle idea generation.