I tried Jerry's method with SeaFoam and the scooter wouldn't start. I pulled the body panels, pet tray, and carburetor. The main jet and idle/emulsion jet were completely plugged. The pilot jet [hidden under the diaphram] had a little film on it. I cleaned the jets with a few strands of fine copper wire and reassembled the scooter. A couple of squirts of carb cleaner were shot into the intake to get the engine running and draw vacuum on the petcock. It didn't want to idle correctly until I rode it around the block but it now idles and runs well.
Lesson learned, drain the carb every Winter.