Remodeling a bedroom in a 1980s townhome. The home was set up with switched outlets and no ceiling lighting in most rooms. The bedroom in question does have 12/3 cable w ground to the ceiling from the switch box, but my parents are set on having a fan without a light in that location. In essence, the red cable isn't being used for the fan, and we'd like to get light to a different ceiling location. I have access to the fan j box from both below and the attic space, but the 12/3 cable is tied to studs and run through ceiling joists, so I cannot pull new lines from the switch without tearing apart walls/ceilings.
My question is whether or how I might try to jump off of this unused red(hot) for a second ceiling fixture. The switch box has room for another switch; it currently has a switch for the outlets, the fan switch, and an empty space, as the old fan had the light and fan switched separately. For the new light, can I just run 12/2 w ground to the new light location from the fan j box, attaching black to red and white to other whites. I guess I'm not sure if it's okay to run two separate fixtures off of the 12/3 of the fan like that, or if it would even work.
I can figure out a smart switch fix on another circuit from the attic, but I'd prefer everything be hard wired and on the same circuit. Any thoughts would be appreciated.