The first company that I know of that attempted to win single-pilot certification for a business jet was Lear Jet with its original Model 23. Bill Lear imagined his speedy little jet as very much a personal airplane, unlike the Gulfstream, JetStar, Hawker 125 and Sabreliner, all true corporate airplanes that the giant airplane companies were delivering in the early 1960s. Maximum certified takeoff weight in the Lear Jet 23 was set at 12,500 pounds so it could qualify under the small aircraft rules. The company did win certification in the small airplane category for the 23, but after FAA flight testing the agency ruled that a second pilot would be required. Following models of the Learjet were certified in the transport category and single-pilot approval has never been awarded, or even requested, as far as I know.
When Cessna developed the original Citation 500 in the early 1970s the airplane was approved at a maximum takeoff weight of 11,850 pounds, which qualified for small airplane certification, but it was certified in the transport category and required a crew of two. The improved version Citation I-SP that came along in 1977 was certified in the small airplane category, along with the larger Citation II-SP, and was thus eligible for single-pilot operation, which the FAA approved.
The maximum takeoff weight being below 12,500 helped to determine the rules of certification, but what Cessna really did with the I-SP was convince the FAA that the airplane had a low enough workload that a trained single pilot could handle it safely. To fly the I-SP with a single pilot you had to have a boom microphone for hands-free communications-somewhat uncommon 30 years ago-and a fully functioning autopilot. There was also the quaint requirement for a transponder ident button to be mounted on the control wheel. In those days we would ident on almost every controller handoff.
In the case of the Citation I-SP and II-SP it was the airplane that was approved for single-pilot flying, not the pilot. There was only one type rating-the CE500-that allowed a pilot to fly any of the Citation models at the time, including flying solo or as part of a crew. The entire focus was on the airplane, not the pilot.