Open this photo in gallery: Gov. Kristi Noem of South Dakota introduces former U.S. President Donald Trump during a campaign event in Rapid City, S.D., on Sept. 8, 2023.JAMIE KELTER DAVIS/The New York Times News Service The contest to become the next U.S. Republican vice-presidential candidate has to date featured public proclamations of doubt about the results of the 2020 presidential election, numerous fundraisers – one disguised as a poll – and at least one dead dog. For months, conservative aspirants have sought to elevate themselves into the country’s political firmament by appealing to Donald Trump, the man already campaigning...