To emphasize that he is the evil twin, almost all of Gils Brady's scenes are accompanied by the familiar "Monster's Rampage" cue from Frank Skinner's score for "Son of Frankenstein," which Universal used constantly throughout the 1940s.
The title is a bit of a misnomer--the entire film is set in or near Triple Creek. Gils Brady may indeed be from "Red Butte," but it's never mentioned even once.