How do you run the breakaway cable to the tow vehicle?

I use a good quality caribiner (not the cheap ones they sell at the checkout!). I attach that to the loop in the end of the cable and then attach that to the frame of the TV. I keep it separate from the hitch, yes the chances of a hitch failing are very high, but I still want it attached separately. On my Excursion I attach it to the safety chain slot in the bumper. When I had my van I installed a stainless eye bolt into the frame and attached it there.

And , no, you don't want it through the chains.