Set the session timeout in Splunk,
When time-out and return to the login screen,
Where is the log output when logging out?
What is the message when it is output?
We were trying to answer this same question and came up with nothing. There does not seem to be a log anywhere that shows a session getting reaped.
An example of a search I ran is:
index=_internal sourcetype=splunk_web_service | stats count by reason