Electrical – add a light fixture (with a switch) to an existing switch/outlet circuit

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I'd like to drywall/finish the 'closet' under my stairs, but I'd like to add a light fixture with a switch inside the closet first. Inside this closet already, the back of an outlet box and the back of a light switch box (and wiring between them) are accessible. That switch, which I'll call switch #1, toggles the outlet, which is for the room adjacent to this closet. I want to add a 2nd switch, inside the closet, which toggles a light in the closet, independently of switch #1. Is this possible? (EDIT: Can someone explain and/or show me with a diagram how this might be possible?)

The wires in the circuit are 14/2 with ground.

Basic representation:

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I have a very basic understanding of circuits and I know that black is generally hot and white is generally neutral, so here is what (I think?) is a more correct representation of how it's already wired:

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Best Answer

You'll need to tap power at the receptacle box

Since power is coming in at the receptacle end of this circuit according to your diagram, you'll need to tap power to the new switch and light there, as that's the only place in this you'll find always-hot and neutral -- any point from the existing outlet to the existing switch won't have neutral, just always-hot and switched-hot.