You have 2 choices:
Add a battery to the trailer to power the lights or:
Bypass the under-hood relay to wire the charge line as always hot (like a GM.)
Yes, with Fords the charge line is hot only with the engine running. The dealer is wrong.
2012 EB 4X4 SCAB XLT 3.55's w/ Chrome, Convenience, and tow package
Pulling a North Trail 21FBS