1st, are you running a ground wire to the trailer chassis?
2nd: If you have running lights @ the "brake lights"(tail lights), it sounds like a bad connection from there up to the side markers. I've come across this before, but it is hard to say with certainty without crawling under there and following the wiring path. If you are getting tail lights at the rear, the problem isn't in the plug, or the lead vehicle. Hope this helps; electrical problems suck!!!