The Daytime Running Lamps (DRL) Module is located under the left side of the IP (Instrument Panel), taped to the IP harness, as shown in the diagram below.
I agree that it can seem like a lot of work to debug a problem in an electrical system, especially when electronic parts are concerned. This is the disadvantage to "advanced" control systems - I like "simple" circuits where individual components can be tested and replaced as needed.
If the light burns out, you would have no indication that the parking brake is stuck on (if it actually is some day), and you could heat up the brakes. If it is an actual LED, it would draw very little power and may not burn out for years. But the schematic uses a symbol that indicates it is a "regular" bulb, so it will draw more power and it could drain the battery after several days or more without starting the vehicle. I do not have the current rating for that particular bulb, so it would be hard to say how long this would take. Worst case - the battery would be drained repeatedly and you would have to replace the battery more often than expected.
Now - after looking at this some more, and seeing a picture of the connector for the DRL module (below), I am kind of starting to suspect the DRL module itself, or maybe some of the pins are shorted at the connector.
What you could do is isolate Pin E, which should be supplying the "Ground Path" for that bulb (according to the schematic). You can isolate this pin by placing Scotch tape over the contact with pin E and see if the light goes out. You should be able to do this because the DRL module is supposed to be a little "PC Board" that plugs into the connector. Make sure the tape only covers pin E.
What I have done in the past is to place the tape on the PC board, and then trim it with a razor knife so that it only covers the contact that I want to disconnect. Then carefully plug the module back in, so that the tape stays in place, and see if the light is out. If so, the DRL module may be shorted in that area.
I priced the DRL module (probably dealer only part) and it is about $65 (USA version). Kind of pricey, but it is a "special" part, and if it fixes your issue, it would be less than having to take the vehicle to a dealer to fix it. OR, you could just leave the tape in place to keep the light off, but then you would not know if the parking brake is ever left on.
Please let me know what you find, and what you decide to do.
Take Care, Greg A.