If you can hear a buzzing noise, then, your wiper motor, or the linkage is jammed, to some extent. Or, possibly, the gears inside the wiper motor are jammed, or stripped. Most gears in a wiper motor, today, are made of plastic. So, you can probably guess, that, it doesn't take too much to wreak them, at all. The wiper being frozen to the glass can be just enough to take out a gear, or more. There may also be a fault, somewhere in the wires, that run from the rear wiper motor, to the rear wiper switch. There may also be a fuse or a sensor, or a relay, that may be bad as well. Do your main wipers work? Some cars have a trace-circuit like material, that is attached to the rear window, and, this material is linked to the wiper motor, itself. This material takes the place of the regular wires, that most cars have. This material is different from the rear defrost strips on the rear window, as well. It is usually located directly behind the rear wiper motor, and, may be hard to see. I would say, that you may need a rear wiper motor. They really aren't worth rebuilding. Perhaps, you may be able to find a used one, in the local junk yard. This route would be cheaper, than a new one. However, with a new one, you are assured of a warrenty, At least.