I wish I could split it at the switch, but apparently the line for the fan runs after the light.
Well, this seems to be exactly what I want to do: Request for ideas to smarten a recessed light - #20 by neerav.modi
Shockingly I do. I was quite surprised, seeing as the rest of the bathroom appears to be from the 60s (no neutral wire, single wire for both fan and light (fan likely added later), etc)
