And to answer your next question . . .
ef_multiple_submit is on line 412 of assets/snippets/eform/eform.inc.php (in the version of eForm I have, anyway).
There’s a debug line just above that. If the $debug parameter is set, it will print out the hash values for the current message and the previous message (stored in the session variable). eForm saves a hash of each message in a $_SESSION variable and compares a hash of the current message against it to check for re-submissions.
I’m going to guess they’re both blank, but I don’t know what would cause that.