How to capture IFS Session's Logoff timestamp

have you tried history logging on FND_CLIENT_LOGON_TAB

I looked at that table and it only has a LOGON but no LOGOFF timestamp, which is the one I am after.

You can use the history log both ways.

   SELECT logons.username,
          logons.time_stamp  AS logon_date,
          logoffs.time_stamp AS logoff_date
     FROM history_log_tab logons
LEFT JOIN history_log_tab logoffs
       ON logoffs.keys         = logons.keys
      AND logoffs.table_name   = logons.table_name
      AND logoffs.lu_name      = logons.lu_name
      AND logoffs.history_type = '3'
    WHERE logons.table_name   = 'FND_CLIENT_LOGON_TAB'
      AND logons.lu_name      = 'FndClientLogon'
      AND logons.history_type = '1'
 ORDER BY logons.time_stamp DESC;

I doubt FND_CLIENT_LOGON_TAB can be used to accurately capture logoffs.

Record from the table is deleted even when the user is idle.