I've acted as your post suggest. Before doing that, I've also also used the Anti-theft website to notify this computer is not lost (just in case the emails are being sent daily when no reply from user is detected).
Then I activated the logging, powered off the computer, loggen on (as my password-protected user), disabled logging and then checked my email to make sure there was a new email from Eset Anti-Theft.
Then I used Eset LogCollector to collect logs of almost all.
I'm not very happy about publishing here such complete logs of my computer, since they will reveal ip address, hostname, users, and such.
I'm adding almost all categories since there is no category called "Anti-theft" inside Eset LogCollector.