I have a switch box with two switches. I'd like to replace one of them - a single-way switch controlling a light in the hallway (which is controlled by no other switches) - with a smart switch. The smart switch requires a neutral wire, and there is not one present in the box. The box has cables for the other switch (the secondary end of a 3-way with switched hot and 2 travelers), and the cables for the switch I want to replace (an always-hot and a switched-hot).
It's not very far to the light: my plan was to get the ~10 feet of insulated wire that would be required, and run a single wire up through the box into the attic (following the wires that are already there), then to the light fixture where I could tap neutral.
Reading about it, it seems like single-wire runs in free air are prohibited (I'm in the US, the construction is early 2000s). I've come up with this plan instead, and I wanted to know: (1) Is this an acceptable alternative? (2) Is this necessary or have I misread, and I could just run a single neutral?
My plan: I can get 10' of 14/3 (it's the cheapest thing by the foot that I can find available at my hardware store... I could get 12/3 for a little more, but there's not 14/2 or 12/2), and that'll be enough for the run. Patch white into light fixture's neutral, unplug the fixture's switched hot and instead connect the red conductor in the 14/3. Wire the bare copper to ground, obviously. Take the old switched-hot line and cap it. On the switch end: run the new cable into the box, tie bare copper to the GND there, tie the switched-hot (red) to the output of the smart switch, and then I'll have my neutral. Take the extra conductor (black) on the 14/3 and cap it on both ends.
I'm worried that this isn't quite right, either, since apparently the current in a cable needs to be net 0: does that mean I need to find where the always-hot is coming from into my switch, and wire that to the black cable in the 14/3? If I did so I would expect I should cap the old always-hot on both ends, but I don't know if it goes and connects anywhere else.
I appreciate your help!
Side note: the GND in the switch box gets pulled in and just kinda... seems to sit there, maybe touch the wall of the box - but doesn't seem to be directly connected to the 2 switches chassis/ground: is that kosher?