Hi Dario,
thank you for taking time and effort to provide complete answer. I erred by excluding critical proviso in my question - I should have written "How to force graceful administrator logout?"
My issue is when a fellow administrator is adamant that he logged-out, yet, I don't see "end=" message in SYSLOG or /var/log/audit .
Every enterprise-grade device has a means to force (graceful) administrator logout - for instance, in FortiOS, "execute disconnect-admin-session". Is it unreasonable to expect same in BIG-IP?
R's, Alex
PS. "Usernames connected through SSH can be checked by 'who'." - I believe F5-sanctioned method is "w" command.