Lighting, Light Fixtures, Ceiling and Exhaust Fans - How to Add Second Switch for New Light

(I posted this in A/C- D/C Electrical, but also posting here)

I have a single pole switch controlling a ceiling light. The single pole switch is fed from an end-of-the-run wall receptacle; it is wired with 14/2 cable (with ground). The single pole switch has a black wire attached to each of its terminals (one black from the receptacle/line; the second black to the existing light/load); the two neutral wires are wire-nutted together in the box, as are the grounds.

I have replaced the existing singlegang switch box with a 2-gang box and would like to add a second single pole switch to separately control a newly installed second light. Each light would have its own individual single pole switch, both switches mounted side-by-side in the same 2-gang box.

I have studied my DIY book and drew up a wiring diagram, but wanted to get a second opinion. Can you tell me how to extend the wiring from the existing switch to the new switch and new light?

My plan is to disconnect the black hot (line) from the existing single pole switch, and wire nut two short black pigtails onto it. One black pigtail will be reconnected to the existing single pole switch, with the second black pigtail connected to one terminal on the new (second) single pole switch. The black wire running to the new light will be attached to the second terminal on the new single pole switch. All neutral white wires will be wire nutted together in the 2-gang box, as will the grounds. Does this sound right?

Thank you.

Double post. Answered in electrical.