Sounds miswired to me. LittleJon's post about adjusting the dimmer may sound
odd, but if the stereo is wired correctly it will have no effect with the
driving lights off... if it adjusts the panel lights you can be sure it is
miswired.
The symptoms you describe probably come from the panel dimmer thinking the
driving lights are on. That would be from the stereo installation
backfeeding power from the stereo into the lights. Ditto with the headlight
click... I expect the dimmer wire and one of the power wires are swapped in
the stereo wiring.
Mike