I would clean it up with a mild degreaser (CRC Professional Degreaser wallymarts) or CRC Electronics cleaner (any parts store). I would not use Carb, Brake, or Throttle Body cleaner; they are too harsh and can damage plastic and rubber components. Be gentle with the float; it's some sort of ?plastic that can get brittle with age.
That the light is coming on shows that it's working. IME it first comes on when the engine is about a 1 quart low and initially it will only come on for a few seconds when you first drive out in the morning then will go off. As you continue to drive over the following days/weeks and the level goes down further the light will come on and stay on longer. Eventually it will stay on all the time when you get around 1-1/4 to 1-1/2 quarts low IME.
There is a test procedure in the BE (Body Electrical Systems) of the FSM) but it requires the sensor to be in a hot oil bath at 140'F (by the book). Basically it should show continuity when the float is up and no continuity when the float is down.
Have you had to add some make up oil between changes?