One controls the vent used and the other controls the temp. It's not fool proof, but after it stops self-clicking, try switching the vent to a different option and wait 30 seconds. If it stays quiet, try changing the temp from full hot to full cold, see if the noise starts then.
Honestly, for how cheap the Dorman replacements are, I'd just do both. Chances are good if one is bad the other isn't far behind anyway, lol.