Jakenut-
OK, I unearthed my Ford spare parts. I found a Ford brake controller pigtail of the correct type. Lo and behold, there's a label on it near the connector that says "Connect to instrument panel feed," which means "plug this end into the correct trailer electric brake connector under the dash." I would have hoped that Ford worded it more clearly, but ...
I am more certain now that you will find the red wire in the pigtail spliced to the orange and black wires, done by a prior owner.
If that is the case, you will want to use the original pigtail, with the splice, and attach your LED to the blue and white wires in the pigtail, and call it a day.
Plug the original pigtail back in. With the engine running, check the one o'clock pin of the 7-pin coach hitch connector for 12V (diagrams
here). Then, shut off the coach, disconnect the original pigtail. With the engine running, check the same pin. By my hypothesis, it should be dead. If you want to keep a working 12V charge line, use the original pigtail.
Save the pigtail you bought for when you want to tow a trailer with electric brakes. Splice that pigtail to the trailer electric brake controller wires, swap the pigtails at the connector, and you're in business.
If the red, orange and black wires are not spliced, well, I'll have to come up with another hypothesis!