Jira Email This Issue (JETI) logs a lot of information to the Jira log files. However, to make this information visible you need to do the following:
Add a logger.
Monitor the log file.
Adding a new logger
Go to Jira Administration --> System --> Logging and profiling. Scroll down to Default Loggers and click Configure a logging level for another package and set the fields as shown in the image below:
This needs to be done every time after Jira starts up. The new logger will enable the output from Email This Issue to appear in the log files.
Monitoring the log files
The most common way to monitor the log is to access them in the files system under the Jira Home directory and do some log file tailing, e.g. tail -f atlassian-jira.log
Another, more convenient method is the following: Use Last Log for Jira that is a free add-on available at the Atlassian Marketplace. This tool reveals log files to Jira administrators without having to access the server Jira is running on.