Left Arrow plays the Scoggins theme which is used in most of the games puzzles, but, if I remember correctly, not Scoggins itself for some reason. Space plays Unresolved Mysteries, the piano theme, a.k.a my favorite track of the game. Right arrow plays Secret Agent Tethers, the theme used on the main menu of the game and is the first thing you hear every time you boot up Puzzle Agent.
Puzzle Agent 1 and 2 are from Telltale Games and based on characters from Graham Anabelle. This great soundtrack is owned by Telltale Games and composed by Disasterpiece, Jared Emerson-Johnson and Nick Mastroianni. If you guys want, I can do the rest of the soundtrack!