Don't ground 3, that is 12 volts and will blow a fuse! If you mean connect 3 and 5 together at the black relay, that gives 12 volts to the fan motor. 3 and 5 at the green will connect 12 volts to the fan resistor, there could be a problem there. The pin 3's in the sockets
are just 12 volts, source of power, the relay clicks on and sends the power to pin 5 which leads to the motor circuit. Maybe there is a way to scan you an image of the diagram. I will see tomorrow.