On the 03 Superduty, the trailer running/park lamp relay is integral to the Central Junction Box (fuse/relay panel rt side kick panel). It is not a serviceable replacement except by replacing the whole panel.
The alternative (if the relay has indeed failed) is to wire a generic relay around it to perform the same function.
There was a discussion a couple of months ago about this in which the owner did exactly that. Perhaps you can poke around and locate it. :edit: Here:
http://www.ford-trucks.com/forums/71...ring-help.html
Also check fuse F38 in the same box. It supplies operating power for both the running and backup lamp circuits.
Steve