Protecting Individual Sovereignty Through Our Laws Act or the PISTOL Act This bill modifies the definition of rifle for purposes of the National Firearms Act to exclude from such definition a pistol equipped with a rear brace or rear attachment designed to assist the shooter in controlling the pistol. The bill also directs the Department of Justice to amend applicable regulations governing pistols to provide that the presence or absence of rear mounted braces or attachments that can assist a user in controlling the pistol shall not cause a firearm to be considered a pistol.