Here's a link to a PDF document
containing a 2014 E-series trailer wiring diagram. The diagram is on sheet 13 of the document.
Per the diagram:
1) Fuses F17 and F48 are in the trailer turn/stop lamp circuits
2) Relays 37 and 38 are in the trailer turn/stop lamp circuits
3) Fuse F57 is in the trailer running (park) lamp circuit
4) Relay 6 is in the trailer running (park) lamp circuit
This completely agrees with the owners manual information you posted.
On that same page you can see the two connectors I mentioned and the 7-pin hitch connector. By tracing the signals you can determine which pin on the 7-pin connector should have which signal.
Of course, the 7-pin connector pinouts are "standard," so here's a link
to a web page that shows the standard (look about half way down the page).
Have you checked each of the fuses and relays listed above? From your initial post, I couldn't be sure.