If the front AND rear lights come on then its not the DRL's that are on(would be really bright at night) but the side lights.
Do the DRL's work correctly during the day, all other lights off?
Are the lights turned off normally?, not left "on" when the key is removed?
My first guess given the age would be the rear hatch wires shorting out turning the lights on, does EVERYTHING on the rear hatch work as expected?