Which piece of information is required regarding the shop's management in the application?

The requirement for the license number of the person in charge in the absence of the owner is essential for ensuring proper management and accountability within the shop. This information is necessary because it designates a responsible individual who is licensed and qualified to oversee operations when the owner is not present. This regulation is crucial for maintaining standards of service, safety, and compliance with state laws.

Having a licensed individual in charge helps ensure that all practices within the shop adhere to legal and health regulations, which is vital in the beauty industry. It also provides a point of contact for regulatory bodies and clients in case issues arise. This way, the shop can operate smoothly, even without the direct oversight of the owner, minimizing risks associated with management absence.

The other options, while important in various contexts, do not specifically address the management structure and accountability in the operational context of a nail salon.