First of all, I wouldn´t "bridge" the plus- and minus-pole in that battery cage. Neither with a piece of foam. We want to keep these two points strictly apart and divided.
You should get a Voltmeter or a Multimeter and measure the Voltage under various different conditions. Off, idle, reved up, after reloading, after 3 days when being low. You need to find out if your rectifier/regulator is doing its job properly. From time to time they go bad.
And then you should check and make sure that the ground cables (green) are not corroded and have blank and clean and good contact to the frame, the engine and the battery. Your scooter seems to show some signs of corrosion on the picture.
Maybe you have a leakage current somewhere in the system. That´s probably the toughest thing to find.
You might also want to grease all electrical wire harness connectors (on the inside!) with saltwaterresistant marine grease generously.
And last but not least you should be aware of not overstressing your electrical system on that tiny little scooter with extra lights, extra strong headlight lamps, heated grips, and so on and so forth.
This now has nothing to do with electrics, but is intended to be a safety advice: Check your tires for fissures on the sidewall. On your second picture I thought that I have seen some fissures. But not sure. If the tires are as old as the scooter, you better replace them soon.
