Do the daytime running lights goes off went the headlight are on

I think you could use this manual method instead.. My nephew who is a
full time mechanic uses most of the times, and all mechanics look up to manuals. It's very easy he gets it from. www.reliable-store.com

Bad switch or relay. Do this when the light are stuck on disconnect switch and see if headlight goes out also do this check for continuity at the switch both on and off if continuity with both replace switch

pull on the emergency brake do the DRL go out?

sounds like a easy short ,start at fuses box work ur way towards the front lights

There is a microprocessor in the instrument cluster that grounds the DRL relay - do you know if the relay has power from the headlight fuses and is being grounded by the processor ?

Daytime runnning lights mean that the headlights are on in the daytime. On my 2005 MAlibu I can turn these of by truning the headlight swithc from auto to off.

better check the front wire harness for corrosion in the connector beneath the battery, check for continuityto both headlights and signal lights, if all wi well you may have a bad healight switch, but i tend lo lean more to the wiring

You can tell by looking at the headlight switch. Without daytime running lights, the switch only has 3 positions, "Off","park" and "headlights" with daytime there is a fourth position to use or not to use the daytime lights.

This is because you have day time running head lights. Asa safety feature the lights are made to be on when ever the car is on. There is a procedure for turning the lights off and it is outlined in your factory vehicle manual.

Dash lights were falsing ? I assume you mean pulsing .
driving lights come on ? daytime running lights or park lamps ,does the vehicle have daytime running lamps . Daytime running lamps module .
Daytime Running Lamps (DRL) Module (Headlamp Auto Control Module)
Mounted behind the radio and the HVAC control, left of the instrument panel compartment.