Tim Walz, a former high school football coach from a tiny town, has folksy sayings and a camo cap. JD Vance shot to fame with “Hillbilly Elegy,” aiming to speak for parts of rural America that felt left behind. Both parties — especially with their vice-presidential candidates — are trying to convey to rural Americans that they are not forgotten. This comes after Democrats have seen significant erosion of support in rural areas. How have Republicans grown their rural advantage to historic levels? Can Democrats do enough to remain competitive in 2024 — especially in places like Mr. Walz’s former congressional district? In the wake of the vice-presidential debate, The Run-Up looks at how both parties are trying to reach rural voters — with their vice-presidential candidates and their messages.