The electrical on these are pretty taxed from the factory. The factory battery IMHO is undersized from the start. I would do as above suggested and go with a group U1 for a start and if that still doesn't keep up put a 11 pole stator on it.
For the brake light I agree it's most likely the brake switch on the master cylinder. It's easy to test. What tools do you have, a multi meter, test light?
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