The center pin of your seven way plug is for the reverse lights. There is probably no wiring going to the center pin of the trailer side connector or it dead ends in the junction box the pigtail ends in. If you run wiring from the junction box to the tail lights and install tail lights with an integral backup light you will now have backup lights.
I would not bother if it was me as my unit came with backup lights and they do not add anything to the backing experience.
You might be better off replacing all the lights with LED fixtures to make your lights lots more reliable and trouble free.