Penebaker is an advocate for universal background checks for gun sales, including private and online sales. According to Penebaker, coordinating the federal, state, and local governments with healthcare professionals and insurance providers to establish better long-term mental health care for those who need it. During his campaign, Penebaker pushed to model federal legislation off Wisconsin's recently passed bipartisan domestic violence law, the SAFE Act, to keep guns away from domestic abusers. Penebaker also pushed for firearm restrictions for suspected persons on the federal no-fly list and other terror watch lists, while supporting an appeal process in case a name has been added to such lists in error.
