Actually, speaking as a teacher of American History, the classic Trench Broom was the old Winchester pump shotgun ... I forget the model number but it sported a bayonet and a hammer. That was WWI and I think it predates the Thompson.
The Thompson was often called the Chicago Typewriter because it "wrote" so many obituaries during the roaring twenties. In fact what do you think made the roaring twenties roar? But the Thompson was originally marketed by mail to rural farmers for "pest control." I'll bet the landowners along the border to Mexico could still put it to that use....
The shotgun in question was the Model 97. Hammer on the outside and it had tendency to go off when you didn't want it to after it was used enough to wear a bit, however, it was very useful and I saw quite a few of them when I was a kid in the 1950s.