Glad you confirmed the actuator is working.
Not only should you clean the connector at the sensor, but also jumper the wire harness to see if the dash light comes on. If it doesn't come on, it may be as simple as a burned out bulb in the dash.
Then remove the sensor itself and check for continuity across the two pins. There should be no continuity initially and then continuity once you push in the ball at the end of the sensor. If there is no continuity once you depress the ball end this means that the sensor itself is bad. It can be replaced with a cheap Beck Arnley back up switch, or it can often be revived by spraying with your favorite degreaser or contact cleaner and cycling the ball in and out.
Another member recently went through a similar problem but with the center diff sensor rather than the rear diff sensor. The concept is the same for the rear diff actuator. See here:
Issues with differential locker