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It's a fun problem to think about, every time you rightly decide it can't be done you get sucked back in again thinking there might be a way. It can make a difference if you happen to have a proper lighting circuit live in there but that's unusual in the hallway lighting.
I had a naughty solution in my house that I eventually sorted out. Ran a line from a socket on the other side of the wall. That's not a recommendation, I used to lose some sleep over it from time to time.
Cheers, I suspected this might be the case! Time to rethink.