You can don one of two things here.
1) The resistor trick is the cheapest. You'll probably need about a 450 ohm resistor. At the taillight you need to cut either the positive or negative feed to the actual bulb and solder the resistor in between the cut. Use solder don't use a butt connector. Use heat shrink and make sure you seal it up nice. If the wires corrode you'll be back in there fixing the issue.
2) So in the NBS (99-07C, my truck) you can swap out the flasher relay with a LED version. However, I'm looking at the up-fitter manual for your truck and it states that you need to have the dealer reprogram the BCM for LEDs. I don't know what the dealer will charge but i'd wager it's probably more than soldering in resisters. The nice thing about this option though is you can revert back to stock and/or you don't create a potential failure point.
if you're interested:
https://www.gmupfitter.com/pdflists/view/6 it's this PDF:
https://www.gmupfitter.com/files/media/ ... 100813.pdf page A-72.
The link posted above won't work in your truck because you don't have an independent flasher unit. The BCM (body control module) manages the blinkers.