Driver side headlight does not turn off

Looking at the wiring and the control system it looks like there are two possibilities. One is that the headlight wiring has shorted to a power feed and the other is that the vehicle electrical control module has failed and is holding the headlight power on.
Because of the way they integrated all the electrical items into that module the only real test would be to unplug the module and see if the light goes off. The issue there is that you do not want to unplug that module while it is still powered as it can damage it if it is not the actual problem.

If you select high or low beam does it go off on one or the other or does it stay on regardless? If you turn the headlights on does the lamp work on both high and low?