We currently run Jenkins 2.319.3, we should upgrade to the next LTS 2.332.2
http://www.jenkins.io/changelog-stable/
Looks like the Debian package switch from hold System V init to systemd: https://issues.jenkins.io/browse/JENKINS-41218 Maybe we can consume their script instead of our own.
The Debian package can be retrieved from upstream and pushed to our apt.wikimedia.org by following the instructions at https://wikitech.wikimedia.org/wiki/Jenkins#Get_the_package