Switching a fan on/off based on an LEDs current
I suspect the LED circuit looks something like this (resistor values are a guess):-







simulate this circuit &ndash; Schematic created using CircuitLab

You don't see 0V on either LED leg when on due to the current-limiting resistors, and you don't see 3.3V when off because LEDs drop some voltage even at the very low current your multimeter draws through them. 

If you measure the voltage from leg 2 to each of the other legs you should see the voltage drop to zero when that LED isn't lit. If this is so then you could use a PNP transistor connected with its Emitter on Leg 2, and the Base connected to leg 1 via a high value resistor. This could then switch 3.3V to an NPN transistor which turns the fan on.







simulate this circuit