Can't read PWM signal from 2-pin fan header
Your picture shows that you have only connected one line to the Arduino.  You do not have a common ground between the Arduino and the fan controller.  You need to connect the grounds together.
Voltage is like height, it requires two points to measure.  If I point at a hill and I say, &quot;How high is that hill?&quot; that seems like a pretty easy question to answer at first.  But it becomes ambiguous quickly.  Do we want to say how high it is compared to the ground around it?  Or how high from sea level?  Or how high from where we are standing?  You simply can't say how high a hill is unless you agree on where to measure from.
It's the same with voltage.  You can't measure a voltage unless you have a potential that you can consider the 0 point to measure from.  That 0 point is the ground wire.  And as you have drawn the circuit the two boards don't agree on where they will consider 0 volts.