To change debugging levels on the vault without having to restart it, both the PAR Agent and the PrivateArk Server Central Administration can be used. The PAR Agent is specifically designed for various administrative tasks including adjusting settings dynamically. Similarly, the PrivateArk Server Central Administration provides a centralized interface to manage various configurations including debugging levels, without the need for a restart. Editing configuration files like DBParm.ini or using Setup.exe would typically require a service restart to apply changes.