What do you mean with a "correct" voltage divider?
I still wonder how a voltage divider can give me 5V if the 12V PWM is high and there is no current?
One with the correct ratio and the correct absolute values.If you have a voltage and load it with a resistor, you have current. That is ohms law.A voltage divider is one of the most widely used configuration of resistors.https://en.wikipedia.org/wiki/Voltage_dividerOr less formallyhttps://learn.sparkfun.com/tutorials/voltage-dividers
Something lik this x3
Exactly like that.
So I should try to find the common GND of the built in RGB controller and share it with the Arduino and use it as GND for the voltage divider as well?
ReducingIs this troublesome LED different from the others? That is could it be that it is a common anode rather than a common cathode.Otherwise you need to look at the signal on the LED with an oscilloscope to see what is happening to it when you connect the Arduino.
Which LED do you refer to
The one that gives the odd behaviour.
Those LED's are 12V common anode!