Using a slider potentiometer with an Arduino
A1: PC joystick port measures basically resistance of the pot, or basically measures how long it takes to charge a capacitor, therefore it only needs 2 pins out of the slider, as the output is not voltage. Arduino analog input measures voltage and the joystick component outputs voltage.

A2: the slider is a linear pot. The current is however related to resistance by 1/X curve, so current is not linear. There is huge difference when resistance goes from 1k to 2k, but much less differenve when resistance goes from 100k to 101k. Your eyes are not linear detectors but logarithmic. It's complicated, but don't expect linear response for the perceived brightness.

A3: Arduino input measures voltages only, not resistances. Connecting the 2 wires of the linear pot between ground and Arduino input will always read zero voltage. You need to connect the unused third linear pot pin to 5V for it to give out a voltage reading.

A4: Because it is a linear pot meant for PC joysticks, it may only have two pins connected, so it may only be used as variable resistance, not a 3-pin voltage divider like a standard pot.

Also, Arduino analog inputs work best when source impedance is below 10k. The 120k pot as voltage divider would present a 60k output impedance, so readings may not be ao stable.