After 20 years in the oil-and-gas industry, Eric Neece was used to its booms and busts. He wasn’t surprised when he was laid off by GE Oil & Gas in Conroe, Texas, in 2015 after oil prices plummeted. He figured his job would come back when prices crept back up.

He was almost right. The work came back. But Mr. Neece’s former job as a well logger—measuring well conditions thousands of feet underground—was gone. Those duties are increasingly being overseen remotely and handled by automation.

Technology...