BAY SHORE, N.Y. — On a recent Sunday on Long Island, Joe Gaeta sprinted nearly 10 miles over the course of a four-and-a-half-hour workday. Wearing an exercise tracking device, Gaeta put in the kind of day that has become rather routine for him over the last quarter-century: He officiated four Police Athletic League youth football games, jogging across the gridiron more than three dozen times to back up a fellow official’s call. He dashed 100 yards on three occasions to follow long scoring plays and sprinted to the end zone a dozen other times to chase touchdown jaunts of more than 40 yards.