What should be done if both auxiliary lights fail after departure?

When both auxiliary lights fail after departure, the correct course of action involves ensuring safety for both the train and any potential interactions with other trains or grade crossings. It is crucial to prioritize safely reaching a forward point where repairs can be made while also adhering to operational limits.

Reaching the nearest forward point for repairs is important, as it allows for a timely and efficient response to the equipment malfunction. Meanwhile, limiting the train's speed to not exceed 20 mph over crossings is a necessary precaution to ensure safety at these critical points, where other vehicles or pedestrians may be present. This speed limit mitigates the risk of accidents while dealing with the compromised visibility that results from the failure of auxiliary lights.

By combining these two actions – continuing to the nearest point for repairs and restricting speed over crossings – both aspects of safety and operational integrity are maintained, making the choice that includes both these actions the most comprehensive and appropriate response in this scenario.