Previous posts are correct. Test light is the way to test. I would also check the socket with TC unplugged. Make sure you have voltage on the proper pins coming from your PU. If backup lights work on your PU (without TC plugged in) and don't work on the TC when plugged in you are probably correct the problem could be in the plug or socket or wiring to the socket. Keep in mind a loose wire can also be a problem. My concern is about the popping sound when you plugged it in. Assuming your ignition is off and PU lights are off when plugging in seems like there shouldn't be any voltage on those pins, except from the TC battery unless there is a loose or shorted wire in the plug or socket.
Make sure when using your test light pick up your ground at the pin on the plug first. If you then see a problem of no voltage on a pin move to a chassis ground for your ground. A bad ground can be easily overlooked. Doesn't matter which ground you pick up first. Just be aware a loose or missing ground on the plug or socket can be easily overlooked.
