The electric cooling (no AC) fan on our '85 Mazda 626 had fused power (12 V) running directly to the fan, with the interruptible ground path running through the relay. The relay was NC (normally closed), and power was applied to it, opening the gund circuit, when the coolant-temperature sensor detected that the fan was not required.
Thus, the cooling fan circuit was the fail-safe type - that is, if the relay lost power, it would close, providing a ground path and turning the fan on.
I'm finding the schematic confusing on my phone, but I would start with the basics - check for 12 V at the fan motor, and if power is present, I would run a ground wire from the motor's ground terminal directly to ground. If the fan operates, then the grounding relay is bad or is not getting the correct signal to operate, or there's some other fault in the ground circuit.