Can I add a light fixture (with a switch) to an existing switch/outlet circuit?

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:

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:

• Your basic knowledge is correct if you have an available hot and neutral that you can tap and bring into this new area you could install a lamp and either a pull cord type of fixture or for a few dollars more add a light switch next to the storage area. Commented Sep 25, 2018 at 4:05
• Hi Ed, thanks for the reply, I should've clarified and asked specifically how can I accomplish it- as far as the wiring setup goes? The source hot wire seems OK but when I think about connecting the neutral, I feel like I'd be crossing currents and I'm either going to create a short, or the new light is going to also turn on by the existing switch #1 which I wouldn't want. Here's where my confusion is: i.imgur.com/AA6jUsp.png I could pigtail the black hots in the new switch just fine, but where to correctly connect the new neutral back into the circuit confuses me, thanks!
– ps48
Commented Sep 25, 2018 at 10:30
• The neutrals are pig tailed at the switch the hot is controlled by the switch this is correct you are not crossing them but placing the lamp in parallel with the outlet this is the correct way to do it. Commented Sep 25, 2018 at 12:59
• Hi Ed, thanks again. Last question (probably) - My concern was the return current along the white. If source current (black) pigtails at my new switch and travels to the already-existing switch#1, wouldn't the returning current after the already-existing switch (white) touch my new closet light on the way back, even if the new switch is off, after the white pigtail? I apologize if I'm being oblivious here. Here's what I mean: i.imgur.com/Wy42Mx9.png
– ps48
Commented Sep 25, 2018 at 13:40
• @ps48 No, that's not how electricity works. For one, current can't flow "backwards". The voltage on your hot is ~120V (if you're in the US), the voltage on your neutral is ~0V. Current will only flow from 120 to 0, not the other way around. Further, current can't flow through an open circuit. In your 2nd picture, the current will go through the pigtail and back out to the panel (and then to ground). Where you have a question mark, you have an open circuit with the switch off, and a potential difference of ~120V with it on. Commented Sep 25, 2018 at 14:14