I have five male Trimbles named "Joseph"....none of them could have been the "Joseph" for whom you are searching.
I have forty-seven male Trimbles named "William"; none of them fits the one for whom you are searching.
The father of the Trimbles in my file is Robert Trimble, born ca. 1695....his wife was Hannah, b. ca 1696.With Robert's and Hannah's birthdates in those years, it is possible they had a son named William, but if so, I have not found him.
It is possible that Robert had a brother by the name of William, but if so, I have not found him.The Trimbles I have found in connection with my families are the only ones I have entered in my files.