In the fuse panel on the driver's side dash.
Under the dash on the left side.
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.
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.
You didn't mention if you checked/tested the low beam headlamps or not.
To stop running the DRL daytime running lights in the 2005 Toyota Echo the headlight relay needs to be modified. The DRL module on the relay needs to be cut and relay inserted into the harness.
the drl relay is in the fuse box
its in the fuse block under the hood on the drivers side by the battery It is located inside the left front fender,you will have to Loosen the battery and tip it forward to get at the relay,it is about 1 inch square with 4 wires.
take the relay out
The drl relay is located in the back of the glove compartment.
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...
In the european version 2008 facelift is under the clove compartment in drivers sear. Its the C102 relay that's near the fuses of DRL's.