BE-35 pilot reported the engine quit after having selected the wrong fuel tank during scheduled fuel management procedure. The pilot decided to successfully divert and land at the nearest airport rather than troubleshoot in the air.

Narrative

On a pleasure flight around the area. I flew from my home base ZZZ1 to the area of ZZZ. During the flight I was burning fuel from the LEFT main tank per the normal fuel management procedure. As all fuel is returned to the LEFT tank on my airplane. As the flight progressed; I burned fuel first from the LEFT tank; then from the RIGHT tank back to the left tank the to the AUX tank. At this point I had encounter some pretty heavy moderate turbulence and as I was attempting to select the fuel selector back to the LEFT tank I inadvertently selected the RIGHT tank from the AUX position. On my aircraft the location of the fuel selector is below my left leg making it very difficult to see. My aircraft also is equipped with only one fuel gauge and a switch to toggle between left and right tank. As I made my way around ZZZ airport and was turning to return to ZZZ1; the engine quit. At this point I turned to return to ZZZ airport and ran through the engine failure procedure. I verified the fuel in the left tank and thinking I had the left tank selected from before; I did not reach down to verify it by hand. Had I done that I would have caught my error. I was near the airport at this point; so I devoted my attention to safely returning to the airport; rather than further troubleshoot my failure. I made a radio broadcast on the UNICOM frequency and landed on Runway XX. The landing was uneventful and I was able to rollout and clear the runway. Ground support personnel met the aircraft and towed me to a parking area by the FBO. As I climbed out of the aircraft I looked down and the Fuel selector and realized my error. A visual inspection of the right fuel tank confirmed it; I had run the tank dry. After refilling the right tank and selecting the left tank the engine fired right up.The cause of the incident was not verifying the correct fuel tank per the fuel management schedule.Contributing factors:Pilot proficiency in aircraft type. Although I fly a lot it is not in this specific aircraft. More proficiency would have made me more mindful of the unique fuel management schedule of this aircraft; and made me more familiar with the fuel selector by feel rather than visually. Which is more difficult based on its location.Another contributing factor is the fuel gauge design of the aircraft. Having two gauges installed would draw attention to an empty tank and trigger a verification of the fuel selector.Environmental factors; bouncing around in the turbulence made the error easier by causing the distraction during the fuel selection process.This incident has driven home the importance of staying proficient in the different aircraft that I intend to fly regularly. It has also driven a commitment to upgrade some systems and displays in my aircraft.