An actuator gearbox includes a drive shaft including a plurality of gear linkages that are spaced apart along the drive shaft, and a plurality of output shafts adjacent respective ones of the plurality of gear linkages. Each of the gear linkages includes a fixed gear coupled to one of the plurality of output shafts and a moving gear that is slideably coupled to the drive shaft. A bias spring is coupled to the moving gear to urge the moving gear out of engagement with the fixed gear. The mechanical switch moves the moving gear into engagement with the fixed gear on the output shaft adjacent the linkage to thereby cause the output shaft to rotate in response to rotation of the drive shaft.