Make sure that the switch on the top of the steering column in turned off. That controls the running lights on the car. FYI that switch is basically used if you are pulled over somewhere and don't need help but yet you need your lights on and still need to take your keys.
I would start with replacing the head light switch
Engaging your parking brake should turn off the daytime running lights
Bulbs burned out? Dimming rheostat is open? Bad headlight switch? Make sure parking and tailights are working (same circuit)
behind the headlight
Parking / Running light bulbs are inside the headlight housing.Refer to the "Related Questions" below for specific instructions by model year groups.
The parking light is in the headlight assy.
behind the headlight
behind the headlight
Probably not. Many newer vehicles have a similar feature that allows certain lights, usually the daytime running lights (headlight switch is off, but headlights are on low intensity high beam) and related ones, to turn off when the parking brake is engaged. I suspect that you will find that your daytime running headlights do the same thing. It is simply the vehicle 'realising' that the parking brake is on and, therefore, the running lights are unneccessary.
The headlights work on a totally different relay than the parking and fog lights. The headlight relay or headlight fuse is usually blown when only the parking and fog lights work.
Remove the headlight assembly and you will have access to the parking light bulb.
headlight switch is bad