We had this exact problem on an 03 Jetta and it was accompanied by an "EPS" light coming on on the dash. The problem turned out to be the brake switch; ours was under a recall but I don't know which years were recalled. The part is apparently easy to replace if you are handy enough but we had to have it towed to the dealership for replacement. Luckily there was no cost with the recall but I don't know how much it is if you have to pay for it.
Try applying parking brake
the brake light switch on the brake pedal is bad and needs to be replaced. A $10.50 part at parts store.
You don't unless you are parked with the engine running. If you are parked and you want the engine running but don't want the daytime running lights on just shut the car off and set the parking brake then start the car back up. The lights should remain off until you release the parking brake.
The only thing that will work with key OFF is the brake lights,head lights and emergency flashers. Dome light will also work.
I take it you have daytime running lights , if so by engaging the emergency / parking brake the daytime running lights should go off
In this order only. Turn engine off. Depress parking brake. Turn engine on. Lights will turn off. To turn lights back on relase parking brake.
The only way to turn them off is to shut off the ignition, pull on the parking brake lever, then restart your engine. Running lights should be off. Once parkig brake is released, lights will come back on.
engage the parking brake , or shut the engine off
fuse, bulbs
The running lights have a bad ground.
If you are parked with the motor running, engage the parking/emergency brake. Turn the ignition off and restart the engine. The daytime running lights should not be on.
on the brake pedal under the dash is a brake light switch. that when you depress the brake it turns your lights on. you might wanna check that