Dont let me ruin your day but.... Does the truck have seperate brake and turn bulbs,look at the module under the truck, also check your turn signal switch. There is a piece inside to stop the brake lamps from back feeding the front turn signals. Common on older Chevys. Could also be as simple as a bulb installed incorrectly.

Make a dedicated ground to the trailer,do not rely on the trailer ball. You grease that right?grease is an insulater..Good luck