Kip Conforti is hiring for a part-time position at one of two package-shipping stations that he owns in Pennsylvania. He’s filled such roles with high school and college students during two decades in business, but this time his top candidate is a man in his 70s.

Mr. Conforti has grown weary of younger employees who, he says, arrive late for shifts, call out of work often and spend more time scrolling social media feeds than chatting with customers. About a year ago, he tried something different—recruiting people who are more likely to carry AARP cards than the latest iPhone.