I have two trailers. Left turn signal does not work on either of them on my 2003 1500. Same result using the 4-wire flat or the 7-wire round. Fuses all test good. All lights work fine when towing with a friend's truck.

Do I need to start unraveling the wire harness under the truck looking for cut or corroded wires, or am I missing something?

 

most likely the computerized fuse box... common for them to go bad.
inter-working connector problems.

I pulled the fuses for all trailer lights and
I did an aftermarket isolated add on trailer light wiring system....
on my 04 Ram.

way cheaper then replacing the fuse box.

 

Sorry, what is the computerized fuse box? I have tried to do some research, but I keep coming up with TIPM. Is there a TIPM in a 2003?

 

I keep forgetting what its called.. but Yes its the TIPM...

my understanding... there are circuit boards in side the fuse box.. and corrosion damages the connections between the boards...

there is a post here somewhere of someone taking it apart and fixing it...

but buying a new one requires the dealer to program it.

but you should test the wires between the Fuse box and the back connectors for the trailer.
as there are fuses for trailer tail lights and a fuse for trailer brake lights.