Adding 2 client-ssl in 1 virtual.

If I may elaborate, it's the server name attribute in the client SSL profile. Presumably each client SSL profile would possess a different server certificate, with a unique subject and/or subject alt name value. By setting the server name field in each client SSL profile to match the certificate's subject name, the F5 can effectively switch between the client SSL profiles based on the Server Name Indication extension in a client's TLS Client Hello message (start of the TLS handshake).

You'll also need to enable the "Default for SNI" option on one of these profiles, in the event that the client does not present an SNI.