You might save a lot of trouble by replacing the fan relay that has gone bad. If you must do it, wire it series from the battery positive to the switch to the fan power wire. Put the switch where you need it to be. The fan has the same ground and you don't need to add another one.
With respect it's not wise to do this. The thermostatic switch in the cooling system does the job better than you can.
tee into the source wire