Hello,
That's a Brilliant way to load balance the administrator users.
Unfortunately, I don't think there is a way to integrate SEPM with F5 Loadbalancers.
Here are 2 options as what I think you can choose from -
1) In SEPM, there is a concept of Domains, which you can use to delegate administrative authority, physically separate security data, or have greater flexibility in how users, computers, and policies are organized. -
A domain is a structural container in the Symantec Endpoint Protection Manager Console that you use to organize a hierarchy of groups, clients, computers, and policies. You set up domains to manage your network resources. The domains in Symantec Endpoint Protection Manager do not relate to Microsoft domains.
If your company is large, with sites in multiple regions, you may need to have a single view of management information. Yet, you can delegate administrative authority, physically separate security data, or have greater flexibility in how users, computers, and policies are organized. If you are a managed service provider (MSP), you may need to manage multiple independent companies, as well as Internet service providers. To meet these needs, you can create multiple domains. For example, you can create a separate domain for each country, region, or company.
When you install a management server, the console includes one domain. Each domain that you add shares the same management server and database. Each domain provides an additional instance of the console. All data in each domain is completely separate. This separation prevents administrators in one domain from viewing data in other domains. You can add an administrator account so that each domain has its own administrator. These administrators can view and manage the contents of their own domain, but they cannot view and manage the content of other domains.
https://support.symantec.com/en_US/article.HOWTO80764.html
OR
2) Try using SEPM Java Console, which will have Administrators choose their own Servers -
http://<computer_name>:9090
http://<computer_IP_address>:9090
Regards,