Why do I have to fit an additional cable to the brake lights, even though the lights on the trailer already work via the CAN bus leads?

When the CAN bus network is under strain, the signals for the brake lights may be sent with a delay. Additional direct pickup of the signals avoids this. If the CAN bus wires are no longer well-connected while driving, a full functional brake signal to the trailer is still available. This also acts as a safety feature.