The thin black, wild guess, might be for back up lights?
Regarding the ground wire on the side with only 2 wires - you should be able to use the metal skin for a ground - but I would look for/check out where the main ground (coming from the tow vehicle) is fastened up front. That's often done on the first metal cross member, you want to make sure that's a good connection. Not a wad of rust.
Regarding the test light - use it to figure out what the wires on the back of the trailer are doing? Once that's known, that should allow you to hook them to the light assemblies correctly.
1997 37' HR Endeavor, 275hp Cat, Freightliner
03 CR-V Blue Ox, Ready Brake