The converter box that some are talking about is only used if your vehicle has a 3 bulb system for running/parking lights, brake light, and turn signal. Your trailor is set up as a 2 bulb system with the brake and turn sharing the same element in the bulb. I agree its probably a bad ground and its probably on the trailor side since your buddy's lights worked better than yours. You can use a battery charger as a power supply as well instead of the lawn mower that one mentioned by taking the black (negative) and hook it to the frame of the trailor and use the red (positive) to hit the 3 males on the trailor plug. Off the top of my head I can't remember which is which but one will run left turn/brake, right turn/brake and the third will be the running lights
Reply if you need further help