If your trucker is newer it should have a fuse for trailer 12v(power). I would first get(or buy) a multimeter or voltmeter(cheap one is fine). Using the meter, check for 12v at your truck connector. Checking here first will rule out if the problem is with truck or the trailer wiring. Here is a website for wiring diagram of plug-in(you'll have to use either 6 or 7way diagram depending on your plug-in): http://www.etrailer.com/faq-wiring.aspx

"The following is done after all attempts of wriggling and cursing at the two trailer connectors together have failed"

  If you have no power at truck connector, check for fuse in truck, than visually check both plug-ins where they meet for rust, corrosion or broke pins/spades. Than check wiring on truck connector(taking it apart if needed). The connectors on truck and trailer do not last forever and are notorious for being the main culprits. I keep a new connector for truck and trailer in the trailer(with tools/meter to change) if needed. A lot of truck connectors are made to plug into a vehicle harness. I will unplug the line at the harness, and check for 12v in the vehicle harness.  If the fuse is fine and no volts at rear harness, I assume their is a break in the line from front to rear of truck. Worst case, if you can't find break is to run new power wire from front to back plug-in. Can just run wire off battery(with fuse holder,rated for wire, using usually 10-12 gauge wire and 20amp fuse) straight back to trailer connector.

  If you have power at the truck connector, than the problem is with the trailer wiring. Since you have two separate circuits on 12v not working, and your other lights are working, we can assume your ground wiring is ok in trailer(#1 on the list of why don't it work). I would check front to back on trailer starting at plug-in. Remove round cover to trailer plug and pull back round cover(careful to not pull any wires with it). Visually check wiring that its connected to all pins. I will plug it into truck(with cover still back) and with meter check for voltage on backside of plug.

  If still no voltage follow wiring from front to back of trailer where switches for lights are. Pay particular attention to any junction boxes or anywhere power wire has been spliced(either by crimp connectors or wire nuts), these are prime areas for breaks, along with switches and light fixtures themselves. Use your meter and check for voltage at all those locations. Hopefully you'll have found your problem by the time you reach back of trailer. If not, and the gremlin persists, worse case would be to run a new power wire from trailer plug-in to your switches or as far back to where you have good wiring.

 Sorry to be long winded, but hopefully this will give you a start to checking and fixing your problem. Its usually not difficult(unless wiring hidden in walls or metal tubing), it can just be time consuming. The above info is also for non-lq trailers, I've never owned a lq and not sure if there is a fuse box for trailer wiring in lq area. Good Luck.