I'm trying to split an outlet to be half hot. Right now the switch turns on/off the entire outlet. I'd like the bottom plug to be always on and the top controlled by the switch. Now I live in an older house, so I don't see the 14/3 wiring that I see on YouTube and other sites. I know I need to break the tab on the right side, but not sure what wire to put on the lower right prong. I've included a picture of the outlet and switch along with a crude wiring diagram. I didn't include the bare ground wires for clarity. Thanks!
All you need is a short length of black 14AWG and a nut
The always-hot is already present in your receptacle box at the nutted-together black wires with the one white wire coming in. So, once the power's off, take a short piece of black 14AWG solid wire (THHN works), nut it onto the existing junction (you'll probably want to use a new nut for this), and land the other terminal on the spare brass screw on the receptacle after breaking off the hot-side tab. You should also take some black electrical tape and flag the white wire that runs from that junction to the switch at both ends with it while you're here, by the way. Button it back up, turn the power on, and enjoy your half-switched outlet! (What you're doing is "pigtailing" the receptacle screw to the existing junction.)