pretty sure you drew your diagram wrong so not even addressing that diagram.

if someone called me on the phone and asked, I'd say "wire the outlet to the white, black, and neutral of the light fixture"15A circuit you will have 14/2 or 12/2 wire, you must use the same gauge at what's currently used20A circuit will have 12/2 wire

if by any chance any of the wire has a red, it's 12/3 or 14/3 so the above wouldn't be correct. Won't elaborate on that since you haven't mentioned red wire.