Using very low voltage from dimmer switch to trigger 12 volt supply
There are two types of dimmers used in cars. Traditionally, it would be a wirewound rheostat, that would drop some of the voltage supplied by the battery to the panel lights. This is pretty inefficient, and newer cars tend to have PWM dimmers, that work by switching the power to the lights on and off by a variable ratio, but at a high enough frequency that you do't see it. Blot of these methods are used with traditional incandescent panel lighting, and LED lighting that's common now, though using a rheostat with either is also not ideal, since the response of the lighting is non-linear, so the rheostat has to be calibrated to a given load.

The dimmer can be on the high or low side of the lighting circuit, yours is obviously on the low side. Which type it is isn't yet clear, since a meter is likely to show the average value if it's a PWM type. If you set the meter to AC, you might see a voltage at the grey wire that isn't zero if it's a PWM type. Where the dimmer is on the head unit is unknowable, but irrelevant, since you just want to trigger it using the headlight input.

If you're just aiming to trigger the dimmer at position 1, this is challenging, since you don't even have enough voltage present to operate transistor to switch a relay. you can acheive this with an comparator that has a reference voltage  probably midway between the 0V for position 0 and the 0.5V for position 1 to drive a relay (or a transistor, since the current needed for this is likely low). Som filtering on the input would be needed to stabilize the signal if it's a PWM type.