You see blind people portrayed in movies that take place long ago, but never deaf people. I assume it was a mixture of random gestures that may have been localize. Considering writing is out of the question. I am curious if there is a history about this or research done.
First, I cannot emphasize enough that deaf people have been around since well-before the 17th century, and while you might not see them in movies about the past (though, how often do you see deaf people in movies/TV set in modern times?) they still existed, whether they lost their hearing in old age or were deaf from birth or early childhood. There are modern communities with high incidences of congenital deafness, including Martha's Vineyard and the Al-Sayyid Bedouins in Israel, and it stands to reason that these kinds of communities are not new in any sense.
The history of sign languages and other forms of deaf communication are generally not well-documented, with the notable exception of Nicaraguan Sign Language.
Families with deaf members who did not live in communities with lots of deaf people would develop what's called 'home sign', which is basically what it sounds like: an idiosyncratic collection of signs particular to a home. While it is necessarily localized, it's not 'random gesture', and has elements of the kind of structures you'll find in spoken languages. Linguists observed these familial homesigns homogenizing into Nicaraguan Sign Language over the course of several years, after the creation of a school for the deaf in Nicaragua. We can assume that basically the same process created sign languages in other deaf communities.