You can buy the reverse light pigtails from ford and splice them into the existing reverse light pigtails on the truck. It is very simple and straight forward once you buy the pigtails.
The sell the pigtails with socket at orielly I just bought them. You have the trim a little on the socket portion bits it's super easy. You get the ones from ford you will need the socket plus the wiring plug
You will need to razor blade the little teeth things that go Into the lamp, just a little, and it cuts easily and it's cheaper than the ford stuff. The wires are bi directional and the package says ford plug
That dorman pn comes up as a gm headlights connector. That came with the connector and bulb socket that worked? Btw, not saying its not right, just double checking