Is the code you are using to set players invisible running on the server-side proxy?
Also, in eclipse, you can run a program in debug mode just like running it normally. Next to the green run button there should be the same type of button with a picture of a bug. It works the same in that you can select which program to run in debug (client/server).
Debugging is extremely powerful in eclipse and because it is such a large topic there a great amount of resources out there. I probably can't explain how to use it all very well so I'll link you to this in-depth article: http://www.vogella.com/articles/EclipseDebugging/article.html
It is very detailed but you can just skim over it to get the basic concepts.
Finally, just a last note on debugging with the client and server running at the same time. When debugging and your server hits a breakpoint or you manually stop it, the program is paused. If a client is connected it will time out after a few seconds which can make debugging server-side stuff annoying. But rest-assured it is still usable for most things.