OK, the headlight is fixed. It was the fuse. My new harness is insulated/heat resistant so hopefully no more overheating and melting of plastic under the hood.
As for the mysterious part it is still hanging there in pieces and all electrical parts are functioning fine. With that said, I'm not going to ignore an issue that could be a potential safety hazard.
Thanks for the replies and I will keep the thread open to see if we can get a definitive answer on what my mystery part is. It is hard to tell what exactly it is grounding (if it is indeed a ground) because the two wires that go to the part come out of a main wiring group that goes all around the motor.