Your blower reisistor may be dead. I think on flat out the resistor is bypassed. But the fan speed is lowered using the resistor on the first few settings. So if your resistor is not there/blown up then the lower settings wont work.
The relay you hear clicking is providing 12V to one side of the fan, the other side is earthed through the blower resistor depending on switch position.
Take a look in the electrical diagrams in the back of the AE86 body manual and it will become clearer.
Hen