Yes, the ground is the most common problem with trailer lights (or any 12v. accessory circuit...). Next up are the various fuse relays. My Chevy truck (Silverado, 2006) actually has more than one fuse that controls trailer lights so you want to take a moment with your owners manual and find out exactly which fuses to check (modern tech can be a pain....).
Now for your wiring runs. The brown wire on each side of your trailer controls your running/parking lights. The green wire is your right side brake/turn, the yellow is your left side... I just spent a few hours finding and fixing a break in one little brown wire up inside the channel where you couldn't see it... lots of fun. Here are the basics, though... 12v runs have to make a complete circle (all the way out and all the way back for any light to work). So an inexpensive multi-meter is a must have before you start replacing parts and hoping that fixes your problem. The first thing I want to know is whether I've got power where the lights are. Turn on your lights then touch the rod lead to the end of the wire and touch the black lead to ground (with the multi-meter set to 10volts so the needle will jump all the way over if you've got power..). NO POWER, then you start from the plug in on your vehicle and check each stage to see if you have power, the vehicle's plug, then your adaptor, etc.
The last really helpful thing your meter can do for you is to set it on the ohms setting and touch red lead to black lead. The needle should go all the way to 100%. Now touch one probe (either red or black to one end of any wire -then touch the other end to the other end of that same wire. If the meter goes to 100% it's a good wire. Now you have the means to check any wire for breaks and to check any junction to see if juice is getting through... I'm no great technician but with a basic small multi-meter you can hunt down and isolate any wiring problem with just these two features. Hope this helps...