Senator JD Vance might invoke his childhood in a former steel town in southwest Ohio or talk about his time as a student at Ohio State University. Gov. Tim Walz of Minnesota could drop anecdotes about his days as a football coach at Mankato West High School and his enthusiasm for mail-in rebates at Menards.

On Tuesday night, two vice-presidential candidates who hail from very different corners of the Midwest will face off on a debate stage in New York City. That presents a rare and particularly Midwest-specific political opportunity: The candidates could draw on their bonds to the region and try to reach on-the-fence voters in the battleground states of Michigan and Wisconsin, which share borders with Ohio and Minnesota.

“There is a Midwestern identity, and that’s one of the things that both Walz and Vance have been playing on,” said Jon Lauck, editor of Middle West Review, a journal at the University of South Dakota focused on studying the Midwest.

That said, the 12-state region is hardly a flyover monolith, and Mr. Walz and Mr. Vance have different stories to tell.

Mr. Lauck expects that Mr. Vance could speak to one narrative of the Midwest that is “more Michigan and Ohio centered, a little more affected by the unwinding of the old industrial order,” he said, connecting with voters in cities like Detroit and Flint, Mich., that were hollowed out during the decline of the auto industry.

The senator’s 2016 memoir, “Hillbilly Elegy,” chronicled the drug addiction and despair of Ohio, becoming a surprise best seller.