He carries multiple harmonicas in his briefcase. He has played with members of the Dave Matthews Band and the Grateful Dead. And he has been known to show up unannounced at bluegrass jamborees around his home state, Virginia, simply looking to jam.

Meet Tim Kaine, vice-presidential candidate, senator, former governor — and mouth organist.

His time in Virginia has left him steeped in the history of bluegrass and old-time music. Hopping up and down the 330-mile Crooked Road that winds through the heart of bluegrass country in Virginia, he has memorized dozens of standards like “Will the Circle Be Unbroken” and “Man of Constant Sorrow,” along with newer songs like “Wagon Wheel.”

“He’s comfortable on stage,” said Woody Crenshaw, the former owner of the Floyd Country Store, about an hour’s drive southwest of Roanoke, Va., where Mr. Kaine has performed numerous times. “He has a feel for the old-time music of these mountains.”

Mr. Kaine has made music an important part of his political life. He has often “sat in” at bluegrass open jam sessions while campaigning and in office. During his Senate campaign in 2012, he held a promotional contest, “Harmonica With Tim,” in which one lucky person would win not just a dinner with Mr. Kaine, but also a one-on-one harmonica lesson. He had a bluegrass band, No Speed Limit, play his inauguration in 2006 (and he hopped onto the stage for a few songs, naturally).