In the fuse panel on the driver's side dash.
Under the dash on the left side.
Your highbeam is dead, which means your DRL's cannot funtion. Your DRL's run off of your highbeams at about 1/2 the voltage...
I have a 2000 Cavalier that did the same thing with the DRL, and only one of the lights worked when I put on the headlights manually. Ended up being a burnt-out bulb that I had to replace. No wiring necessary.
Most likely this is related to the BCM grounding the DRL relay.
You didn't mention if you checked/tested the low beam headlamps or not.
its located right in the fuse box on the driverside dasboard. its the only black box type fuse in the panel Just know that when you remove this, you will have only one headlight working and an annoying DRL light on your gauge cluster. Unless you know the jump sequence...
DRL are your Daytime Running Lights
The ground ciruit for the headlights is by way of the headlight switch , the lights always have power
DRL stands for Daytime Running Lamps.
The DRL Module is located at the LH Rocker Panel left of the brake, under and just below the dash. The DRL Module and the DRL Relay are side-by-side.
I ripped up the headlight wires from a little below the driver side headlamp all the way to the other lamp. I found A LOT of connections rotted out. I re-did the connections and viola, DRL's ran again. Also there is a DRL relay on the radiator just behind the hood latch. Try that first. Good luck. If you are speaking of the relay beside the hood latch, its a crash sensor and not a DRL relay.