I agree- it's probably a ground issue. Make sure there's actually a ground wire from the plug to the trailer frame. Some people let the trailer ground through the hitch ball...it works, usually- but it's not reliable enough for my taste.
That said...I once spent 8 hours chasing what I was sure was a "ground issue" on my truck/trailer. Ended up that the converter box (the '97 has amber turns in back, so you need a special converter box to get the right signals) had failed. Nothing wrong with my wiring at all.
Before I spent too long pulling my hair out, I'd grab a multimeter- start on the truck side. Check continuity from the white pin to the truck frame. Then measure voltage between each pin and ground. As stated above, brown is running, yellow is left (yellow line to your left when you're driving down the road), green is right (grass to your right). Running lights should be steady when the headlights are on, yellow and green should blink when the appropriate blinker is on, and both be solid when the brake is depressed.
EDIT: It's been a while since I messed with this stuff...and I'm typing fast. I can't swear to the accuracy of everything above.
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