You could test for reversed polarity, your trailers hook-up wires may be reversed they could be cross wired to ground, i would get a seperately powered coninuity tester & test the system without power - to ground and each bulb. if the ground side is touching the trailer chassis you need to check the + positve wire to each socket they must be seperate and properly wired to the socket from the plug. ~>
(if the system is isolated to it's wires) then you should check for shorts between both your positive conductors at the trailer (Plug) and possibly your hook-up outlet ~ for this you could use the 12VDC tester they sell at the auto or 99=E7 store. make sure you get the correct light/signal output at the vehicles socket, then break it down to your trailers plug/wiring & to the sockets. {you could leave the bulbs in and just see which ones come on when you connect each wire to a 12vdc source at the plug and then wire them back in to their corresponding contact on the plug} having made sure your socket is properly wired of course. Left & Right signals isolated & 2 seperate Stop contacts. if I'm not mistaken, I fixed one on my block not too long ago };-)
Roy