Mostly putting this here in hopes it'll help somebody else. When I set out to wire ours up for trailer lights I couldn't find much helpful information on it. Other than that the dealer wanted about $2k to do it. The most help was found here:
http://mbworld.org/forums/glk-class-x204/538247-2013-glk350-trailer-wiring.html
The important part is this: "Setup that works on my 2013 GLK350 4matic. Curt 56200 PWM-ST Power Converter with Circuit Protection. This is the converter that has the combined Stop/Tail wire. Converts with separate Stop/Tail do not work. I mounted the converter in the left side wheel well. There is a ground bolt and a 12v outlet for power. The PINK wire is the Left turn. BLACK/GRAY is the Stop/Tail. In the right wheel well - the BLUE wire is the Right turn."
The 2013 and 2014 appear to be nearly identical. The same setup seems to have worked, according to my test light. Won't have a trailer until next week (see my introduction post in the "newbie" section).
Anyway. Hope this helps somebody. The install wasn't too bad, except I refuse to use those blue crimp-on wire taps. I cut, twisted, soldered, and shrunk-wrapped all the connections. I like that better.