Is it possible for a user to start/stop their Tomcat installation, or check the status?
Yes. Part of the Tomcat installation is setting up different instances for each user that is using Tomcat. The user would require shell access (jail shell is fine). These commands can be ran through SSH directly or using the Terminal through cPanel. Using the commands below, you can start, stop, restart, and check the status of Tomcat:
[cpanleuser@server ~]cPs# ubic start ea-tomcat85
Starting ea-tomcat85... started
[cpaneluser@server ~]cPs# ubic stop ea-tomcat85
Stopping ea-tomcat85... stopped
[cpaneluser@server ~]cPs# ubic status ea-tomcat85
ea-tomcat85 not running
These should only be ran as the cPanel user, not root.