Bethlehem is a school of gun builders in Pennsylvania, that date back to the late 18th century. Check George Shumway's books to learn more about the various schools, and the names of the gunbuilders that are considered members of each school. Je Kindig, Jr., book ( Published by Shumway)Thought son the Kentucky Rifle n its Golden Age, lists A Verner, the Angstadt Family,Feder, Rupp, Moll, Pannabecker, Albrights, and a J.D. as members of this " school". There are pictures of representative works from each of the builders mentioned.
I don't know of T. Williams, but you can sometimes identify builders by checking with Track of the Wolf. They sell a lot of guns on consignment or gun makers, and may know who this person is.