Unfortunately, your brake controller likely won't display an error for a broken wire on just one side.
If you can't tell by feel by towing & braking at low speeds, your best bet is to park your vehicle and trailer, disconnect your electrical trailer connector (VERY IMPORTANT!) from your vehicle but otherwise leave it hitched and chained, jack up one side of the trailer so that the tire is just off the pavement and can spin freely, and then pull your breakaway cable/pin. This will lock the brakes, which you can test by trying to rotate the tire. Replace the breakaway pin, lower the jack and then repeat on the other side. Try not to leave the breakaway pin out for more than a minute or two at a time.
Note:
- you could wreck your brake controller if you leave your r-pod plugged into your vehicle while doing this procedure
- I suggest leaving the r-pod hitched to the vehicle as an easy way to prevent the trailer from rolling away while its jacked up
- pulling your breakaway cable for a minute or two is fine. leaving the brakes on full for several hours could very well burn something out and/or deplete your battery.
- don't forget to plug your r-pod back into your vehicle before you drive away