Re: vanity light on bathroom gfi
shadow,
There might be local ordinance for existing buildings that you will need to satisfy. Your inspector will have the answer.
In my area, there is the general understanding that an existing 15 amp circuit can be used to install a receptacle in an existing bathroom only when the work occurring in the bath is minimal.
If the plumbing is being reworked or replaced, opening the access to the waste stack, the guidelines require the running of a new 20 Amp circuit.
Also, if 50%, or more, of the wall area is opened as part of the reset of the bath, the room must be upgraded to current NEC standard.
As I understand the thinking, when a room is being remodeled, the related work makes access to wiring routes the best that they are likely ever to be short of a total gut to studs. The price to improve the wiring, while high, will still be as low as it will ever be, and, is most likely to be a small portion of the budget for the entire bath reset.