Welcome to the forum.
I am thinking that there isn't an issue with your trailer as an issue with your tow vehicle. The reason, the left brake and the left turn signal work on the same pin/wire/bulb. So, when you step on the brakes, and only the left brake light will come on, the left turn signal should also flash.
Does your vehicle have a factory tow harness and plug, or did an RV shop add what was needed. My vehicle didn't come prepped since I bought it used, so I had to wire everything myself including a converter box.
Also, living in salt country, I have to change my rear plug every spring due to salt corrosion. You could have issues there, too.
