You will need a fan switch in order for that to work. The sender, in the back of the head, assuming it is for the original gauge, is not a switch. Jet and Hypertech come to mind. Some have set temperatures at which they turn on and off. Others are adjustable.
On the wiring, I’ll guess you should have a hot wire from a key hot source which runs to the low current side of the relay and then from the relay to the switch and a wire from the battery to the high current side of relay and then from the relay to the fan.
You probably have it wired correctly. You're just using the wrong type of part to switch the relay.
Lawrenceville, GA