Final answer:
The first action when a ship's course changes to the right with the gyro-pilot engaged at night is to switch to hand steering, to regain control and prevent hazards.
Step-by-step explanation:
When you notice that your ship's course is slowly changing to the right with the gyro-pilot engaged at night, the first action you should take is to switch to hand steering. This immediate response is necessary to regain control of the vessel's direction and prevent any potential navigational hazards. After you switch to manual control, you should investigate the cause of the course change, which could include a malfunction of the gyro-pilot or a change in sea conditions. If the issue can't be resolved quickly, the next step might be to notify the engine room and call the Master for further instructions. In case of a total steering failure, it could be necessary to shift steering to the emergency steering station, as indicated in safety protocols.