Thank you, Rodrigo..
The settings you suggested didn't make a difference. The IMAP task still behaves the same, logs the same.
I've also tried these:
Log_MailRouting=40
IMAPDebugIO=4
The debug option gave a lot of information, including the IP of the client, but it also filled the log with too much data for every quick connection.
I was hoping to make the IMAP task report the IP just like how SMTP does (directly on the console, and appropriately in an event handler linked to an agent, for example).
I am actually trying to capture the data by an event handler. But without success so far.