Answer
Query the FND_CLIENT_LOGON_TAB table (for example, SELECT * FROM AO.FND_CLIENT_LOGON_TAB) to find the stale session row for the affected user, and delete that row to clear the stuck session. Once the session record is cleared, you can log in again and use the client's own switch-user option to properly change accounts going forward, rather than continuing to hit the 'already logged on' block.