The cord you are describing under the seat of your Yamaha FZ6R is likely the connector for the Battery Tender or battery charger. The Battery Tender is a device used to maintain the charge of the motorcycle's battery when it is not in use for extended periods.
The cord usually has a cap or cover to protect the connector from dirt, moisture, and other elements. The connector itself may resemble a household plug or have a specific shape that matches the corresponding charger or Battery Tender.
To use the Battery Tender or charger, you would typically connect the cord to the battery tender output or charger input. This allows the charger to provide a trickle charge to the battery, helping to keep it charged and healthy during periods of inactivity.
If you are unsure about the purpose or functionality of the cord, it's a good idea to consult your motorcycle's owner's manual or contact a Yamaha dealership for clarification. They can provide you with specific information regarding the electrical components and connections on your Yamaha FZ6R.