Long after government regulators had confirmed the lethal consequences of cigarette smoking, Mike Pence mocked their warnings as “hysteria” in 1998.

“Time for a quick reality check,” he wrote. “Smoking doesn’t kill.”

Long after most members of Congress had abandoned the quaint practice of delivering one-minute morning speeches, Mr. Pence eagerly held court in an empty chamber, musing about sports and Scripture.

And long after Republicans’ war on big government was fading, Mr. Pence defiantly opposed his own party over the creation of signature programs like No Child Left Behind and a Medicare prescription drug benefit.

Throughout his career as a congressman, radio host and governor, Gov. Michael Richard Pence of Indiana, Donald J. Trump’s running mate, has been deeply and proudly out of sync with his times.