There are a few things you can check, but I'll start by saying that now that we know you have a built in factory controller, if you can figure out how to check fault codes I would go there first.
Above is an image of the vehicle side of the 7 pin connector. The left side image is looking into the pin connector on your tow vehicle. First thing is to ignore the center pin as it's for backup lights. Now look at the blades arranged in a circle kind of like the numbers on a clock.
You will notice that the 11 o'clock blade is for a brown wire which is the tail and running lights. 1 o'clock is black wire 12V positive, 5 o'clock is your blue brake wire and 7 o'clock is your white ground wire. You might by now also have noticed that there is no brake light wire for the trailer brake lights. This is because when you put on the brakes your tow vehicle basically just turns on both turn signals but doesn't let them flash. So your brake light wires are actually both the green 3 o'clock and the yellow 9 o'clock terminals.
Set your meter to 20v dc volts (or just dc volts if you have an auto ranging meter).
Apply the parking brake and block the wheels on your tow vehicle. Now turn on the ignition but don't start the engine. Now put the black probe on the 7 o'clock blade and the red probe on the 1 o'clock blade. You should get battery voltage. Write down or remember this number. Now move only the red probe and check all the other pins. You should get no voltage on any other pin.
Assuming that the above tests are good, turn on the running lights and measure from the 11 o'clock pin (brown tail running lights) to the 7 o'clock pin (White ground) You should get battery voltage with this measurement or pretty darn well near battery voltage. Now keeping the black probe on the 7 o'clock ground pin, move your red probe down to the 5 o'clock (blue brakes) pin. You should have no voltage on this pin.
Assuming that the above tests are good, turn off the running lights and turn on the left turn signal so it flashes. Now measure from the 9 o'clock pin (yellow left turn) to the 7 o'clock pin (White ground) You should get flashing battery voltage although many meters are not quick enough to display this so if the numbers jump around it's probably good enough. The important part is the next measurement. . Keeping the black probe on the 7 o'clock ground pin, move your red probe down to the 5 o'clock (blue brakes) pin. You should have no voltage or flashing voltage on this pin.
Repeat the above test using the 7 o'clock ground and the 3 o'clock green terminal and the blue 5 o'clock terminal.
If you get no voltage on the blue 5 o'clock brake wire for any test you are probably good with no shorts on the brake light wiring on the vehicle side.
Turn off the turn signals and running lights and get a helper. If you don't have a helper handy, turn off the ignition until you can get a helper.
Keep the engine OFF, but the ignition on so the warning lights are all illuminated on the gauges. place a helper in the drivers seat and go put your black probe on the 7 o'clock ground and the 5 o'clock blue terminals. You should have no or extremely little voltage. Now have the helper just barely move the two squeeze levers together until you get a voltage reading. Did the voltage jump straight up to 9 volts or more? The voltage should ramp up as the levers are squeezed further and further. If the voltage jumps from 0 to 9+ volts with all lights off and no brake pedal pushes, then you most likely have a controller fault. If the voltage seems to ramp up smoothly with the lever being moved, you controller is probably okay. Just as a check have the helper let go of the levers and step lightly on the brakes until the lights come on. You should get voltage, but probably not more than 1.5 volts as the lights come on.
