Strange. Both my 1991 Dodge pickup and my 2007 chevy trailblazer have 7-pin connectors on them. When I insert a "7-pin-to-4-pin" adapter in them, the 4 pins that I described are the ones carried through to the 4 pin connector, and the back-up lights on other folks's trailers (that had 4-pin connectors) that I have towed all had the backup lights work.

My own trailer has a 7-pin connector, so I don't have to worry about it.

On the other hand, I have wired my CJ7 (with a diode set and a 4-pin connector) so that it's rear lights will work when I'm flat towing it. I plut a 7-pin to 4-pin adapter in the trailblazer factory 7-pin connector, and the back up lights on the towed Jeep work.

Point taken about making sure the key is on and making sure that the lights on the tow vehicle are working while checking the trailer lights.

That being said, both of those turn signal wires are used for hazard flashers, and they're both used for brake lights, and the key does not have to be on for either of those conditions.