Reading the manual, eggPlant plugin for Jenkins, I assume this will install “eggPlant Functional” on Jenkins machine.
No. The eggPlant plugin is just a Jenkins plugin. It doesn’t install eggPlant Functional. And you do not need to have eggPlant Functional installed on the Jenkins master machine – you can have it installed on a slave node.
This means Jenkins is our SUT.
Even if eggPlant Functional was installed on the Jenkins machine, that wouldn’t make the Jenkins machine the SUT. The SUT is the machine that eggPlant Functional connects to and run tests against, and it can almost never be the machine that eggPlant is installed on.
Would this then mean we have to install the VNC Server and the actual program to test on another machine?
Yes, you would need these elements on another machine. It would be a second machine if you chose to install eggPlant Functional on the Jenkins machine. It would be a third machine if you chose to put eggPlant Functional on a slave node. The application to be tested needs to be run on a separate machine (either physical or virtual) from the one running eggPlant Functional.