Yes the battery does drain down with this defect...it was a problem the previous owner had when I bought the car. His solution to the HRW light on all the time was to simply pull out the fuse.
Just changed the Multi-Function ECU and HRW light is off and all seems back to normal and WHAT a easy fix it was too THANK YOU EVERY ONE
I can give her a nice wash and polish now as a treat for being an easy fix