Pull the switch out with the connector still plugged in, now use a test light/metre to see where the power is coming in, and that on each speed setting there is a output wire that is becoming live in only the one position, of the speed setting, so you can determine what is what.
If no joy get a small bit of wire say 6" long strip and solder each end about 1/2", the put one end in power supply, then probe the other wires with other end, you will soon determine what is happening, just be carefull NOT to insert into a grey/yellow wire or brown wire, as these are for the illumination light.
For measure put a fuse in the wire say 10amp using spade connectors etc, unless you have some fuseholder tap ins ?
tabetha