Cleaning the front wheel sensors is a routine maintenance item. I clean mine once a year; they are always covered with crud. You should do this anyway. When the ABS engages, clean sensors will make a difference in how well the system performs.

Your immediate problem, however, is clearly the rear sensor. Or more likely, the WIRING to the sensor. Get the rear of the car jacked up and supported on jack stands at the rear jack points. Go under and visually inspect the wiring, you will likely find that there are a few places where it is compromised (typically where it bends or flexes). The wires from the sensor are attached to it with the usual removable connector. Clean things up and gently unclip the wiring, and follow it up into the car body. Figure out how much of the wiring needs to be replaced, cut new wires, and install the new stuff in place of the old re-using the gray plastic protective sleeve and the connector(s).

No need to remove or clean the rear sensor itself. Sealed inside the diff housing, it should not be dirty.

Wear safety glasses when you're messing about under the car, you'll knock a lot of nasty grit loose while you're playing with the wires, and it's very unpleasant to get any in the eye. Very.

John