The city is home to an Army Proving Ground and a Marine Corps Air Station, fortified islands that nonetheless help shape the county’s law-and-order disposition. Latinos, whose roots in the area straddle two countries, make up 62 percent of the county’s 201,000 residents, and the closer one gets to the border, the more predominant they become. In the city of San Luis, which adjoins Mexico, virtually every resident is Latino.

Not all of them can vote, though, and among those who can, there are many who do not because they are not engaged politically. One thing that makes Yuma stand out is its success in at least one key element of Mr. Trump’s approach to border security: Apprehensions of undocumented immigrants plummeted to roughly 6,000 last year from 140,000 in 2005, after a barrier that already existed was fortified and augmented.

Eleven years ago, unauthorized immigrants would rush at the border by the hundreds, knowing that federal agents could not catch them all. These days, it is mostly Central American and Haitian migrants who are keeping the agents busy, turning themselves in at the port of entry in San Luis and asking for asylum.

“Illegal immigration isn’t something that’s on people’s minds around here, Hispanic or not Hispanic,” said Capt. Eben Bratcher of the Yuma County Sheriff’s Office.

The area’s political balance has been slowly tilting left, as the county’s demographics are changing, mirroring the rise in the number of Latinos throughout Arizona. For the first time since 2004, voters elected more Democrats than Republicans for the Board of Supervisors. Still, “in the Hispanic community, there was a lot of disagreement over Trump,” said Tony Reyes, a county supervisor for 18 years and the vice chairman of the county’s Democratic Party.

“There were some people who judged him by his statements on Mexicans and Mexico,” Mr. Reyes said. “Then there’s those who picked him because of his message on jobs.”