Kwikee Step Problem

I've encountered the same thing with mine when the engine battery was low. If your steps are like mine the clicking you hear is a bi-metal thermal switch inside the motor. The motor is a car power window motor. The thermal switch is used to cut power when the steps reach the fully extended or retracted position. Too much current and the switch opens, the controller senses no current flow and it cuts power to the motor. Only takes a second or so for switch to cool and close then the steps can be operated in the opposite direction.

Your diagnosis is pretty accurate. The low voltage from the battery causes the motor to draw too much current and opens the thermal switch.