Recommend you buy a multimeter. Basic function meter can be had for less than $10, and once you learn how useful it is, you'll use it for many different tasks. There are tons of YouTube vids (even some good ones!) that will walk you through the process of using a multimeter and how to troubleshoot electrical issues on a simple boat trailer.
Recommend you also rig up a single wire, about 20' long, with gator clips on each end. You'll use this to test continuity of the wires, along with the multimeter. Again, YouTube vids can walk you through this process.
I had the same issues on my trailer last year. Using the multimeter and the continuity test wire, I was able to determine that one side had a broken wire and that both lights needed better grounds (the previous owner cobbled together the lights with the wrong kind of lights for a boat trailer.) In the case of my trailer, there were so many wiring issues that it took me a couple hours of "test a little, fix a little, test a little, fix a little."