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Using a TACACS+ server for router authentication indeed provides a significant benefit in tracking user activity across various access methods. TACACS+, which stands for Terminal Access Controller Access-Control System Plus, is designed to centralize the authentication, authorization, and accounting (AAA) functions. One of the key aspects of TACACS+ is its capability to record and track user sessions and activities, which is crucial for security compliance and auditing purposes.

When users access network devices, TACACS+ allows logs of their activities to be generated that encompass all the different access methods employed, whether it be through console access, SSH, or Telnet. This centralized tracking enables network administrators to maintain a detailed record of user interactions with the system, which can be invaluable for troubleshooting, security analysis, and ensuring adherence to organizational policies.

Other options, while they may hold some merit individually, do not encapsulate the comprehensive tracking feature that TACACS+ offers. This capability is particularly important in enterprise environments where accountability and security are paramount. Thus, the ability to track user activity is a crucial benefit of employing a TACACS+ server for router authentication.