Has anybody wired a relay into their blower motor circuit to get more voltage from the high fan position of the switch?

I'm thinking a relay mounted near the fan, pulling voltage directly from the alternator, with the normally closed position feeding the voltage from the resistor to the switch and the normally open position feeding alternator output directly to the fan would work. I think I'd just have to route a wire from the switch to the relay trigger wire to do this.

See drawing (sorry for it being so crude).


Any comments?