Hook up the outlet as you normally would. The red wire would be used as the switched leg back up to the vanity light where it would be connected to the black wire of the vanity light.
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Wiring a plug to a light switch. Wiring a receptacle to a switch receptacle always on. This kind of task is really useful if you have a source of power where you can plug in a light but want to place the switch in a more convenient. Connect the black wire to one of the switch terminals and the black wire going to the light fixture to the other switch terminal. Learn how to wire up a plug in light and switch. You then splice all the white wires and all the ground wires in the switch box together. The black and white would be used for the power for the outlet and the vanity light switch.
Things youll need wire cutters needle nose pliers screwdriver standard light switch 14 gauge copper wiring outletswitch face plate. To add an outlet to a light switch you start by making a pigtail using the hot wire the wire going to the fixture controlled by the switch and a third length of wire. Twist the white wires together and cap them and connect the ground wires to the ground terminal. Install a 3 wire cable of the same wire gauge from the vanity light to the wall switch.