Depending on the vehicle, this could be caused by a couple of things,
1.Daytime running lights turning on, (setting the parking brake on certain car models prevent daytime running lights from activating)
2.Autolights, they automatically turn on when vehicle is powered up but maybe shutdown by the vehicle's ambient light sensor on top of the dash senses sunlight or ambient light. (Shut off Autolights by placing the lightswitch to OFF and not AUTO)
3.Improper parking light connections, (Connections to vehicle must be tested using proper testing equipment, logic probe, Digital Voltmeter etc)
Please provide us with the Make, Model and Year of your vehicle so that we can better help you diagnose this symptom if it is indeed a problem or a normal reaction on your particular vehicle.