In Yosemite, there is a log file here:
...but it's always empty. How do I make the system write events to it, assuming there are any?
Unless you know that you've tinkered with the permissions on the file, it should be:
-rw-r--r-- 1 root wheel 0 Oct 18 11:02 /private/var/log/coreduetd.log
This logfile is empty on the 5 Yosemite Macs I have access to.