Mine has rubber all the way around. Incidentally, I replaced my glass with UV-treaded plexiglas both for lightness and so I can mechanically SCREW my outside control Omni mirrors to holes bored through the 'window'. Gluing anything to glass takes quite an effort because glass almost instantly acquires a molecular layer of water on it; to get any glues to stick you have to somehow scrub the water layer off and bond very quickly. Note also, plexiglas can be tinted at home for pennies, to match tinted windshields & side windows, the same way plastic sunglasses are tinted.
Forming plexi to the compound curve needed is simple & cheap: lay a piece of plexi on top of a glass window and put the parts in Mom's oven. In a few minutes @ no more than 150F, the plexi will sag around the glass which will be completely unharmed. Remove from oven and let them cool without separating the still soft plexi from the glass. When cool, trim plexi as required. I usually make a few at a time because even UV treated plexi stress-cracks from sunlight after a few years. There's an illustrated article in the POCA Archives on all this.