The emergency trailer brake wire is to be attached to the tow vehicle. It should not be attached to other hitch parts. I have mine attached to the hitch receiver which is in turn fastened to the tow vehicle frame. I would prefer attaching it directly to the frame, but do not have any way to do that.
It should only pull the brake when safety chains and ball hitch have become detached. It is not designed to protect the back end of the tow vehicle. It is designed to slow the trailer if it becomes detached from the tow vehicle.
Under some conditions, the brake wire may function if woven through the safety chain. Under other conditions it won't. For safe operation do not weave it through the chain. Make sure it is free and not in danger of becoming entangled with anything else.
eTrailer.com sells self coiling brake wire. Mine is red and works much better than the straight wire that came with the trailer. I had to replace the straight wire occasionally because it tended to get caught in bad places and was cut.
I wish you good luck and happy trails ahead!