I have a 2003 2500hd with the tow package. If you have the tow package the control relay activates tow separate circuits. One for the truck, and one for the Trailer.
The circuit is fused at 10 amps per side (left, right). That fuse block is on the drivers side with the door open (there are three fuse connection points on the Chevy's - one under the hood, one under the dashboard and one on the side of the dash on the drivers side).
Coincidentally I'm having an issue with my turn signal relay - but someone posted the answer for me under the tow vehicles section. his was a 2005, had the same problem and it was resolved.
If you actually have more than 10 amps on either the left or right turn signals, that could cause the problem, but it's fused at 10 amps, so I don't think you're exceeding 10 amps or the fuse would have blown.
