Boat trailer light problem

BeenThereDoneThat.
Panfisher this is a shot in the dark.  Are the connectors for the lights, the snap-on or pinch on type that pokes through the wire insulation?  I'm thinking there just may not be enough contact at that location for both lights to work efficiently.  I'm assuming both tail and turn have the same ground contact. 

Erie Mako
Did the rewire job include a new vehicle connector?
Yes
Yellow - left turn
Green - right turn
Brown - marker
White - ground
Best practice is to ground the white wire near the hitch and run a ground wire back each side to the side markers and tail lights.
Maybe my connection to the side marker is not good.   Will check that out.
 
To me, from experience, the condition you describe indicates a poor ground connection.
 
Out of curiosity, does the tow vehicle(s) have seperate brake & turn signals on the rear?
Yes
 
I have seen the ground pin on the trailer end of the 4 pin flat connectors that were spread open too far and actually not make a connection, even new ones out of the box.
 
Don't rely on the crimpy-squeezy connectors that come with the light kits - better to cut, splice with heat shrinkable butt splices then coat with liquid tape.

EMitch
EAt the end of the trailer harness ground wire, I solder an eyelet to it and drill a hole near the tongue of the trailer, then with a 25' roll of white 18ga. wire from the auto parts, I solder and eyelet to the end of that and run it through the main center frame tube. The eyelets of both ground wires get bolted together through the trailer frame. I cut off enough of the wire to reach from the right tail light, to the side marker, and across the frame to the left frame rail. I then take a 1 1/2" piece of shrink tubing, (I use the type that has the meltable sealing glue inside), slide it all the way up the remaining main wire, past where I'm going to make a connection, strip the main wire 1/2" (without cutting the main wire), strip the right side wire, connect to the main ground, solder and shrink tube, then proceed to the lights. Same thing for the right side marker, strip the ground without cutting through, and with a tag wire with an eyelet, slide the shrink tube past where the splice will be, solder the tag to the right side ground, shrink tube, and then connect the eyelet to the marker ground. That's the way it goes for every light. The self sealing shrink tubing can be covered it you prefer, but is not necessary.