The trailer module/ECU sources it's light signals via two patch cables inserted into the looms at the tail lights. There is a patch for each side, the brake light signal is sourced from the RHS tap. You could also check for a stop signal at the trailer connector.
If there is a problem with the way either or both taps have been installed then it could be possible the brake light signal may not be passing through to the vehicle lamps.
Check the connections on the taps, and if you want to eliminate the taps then temporarily remove them and plug the main loom directly into the lights as they would be on any vehicle without the trailer ECU.
If they are still not working check the voltage in the connectors on the main loom in case any pins may have been damaged in the installation. Stop signal is pin 4, red/black wire on the RHS & grey/black wire on the LHS.