Unless I am totally misunderstanding, you need some kind of submit. If there isn't, the page will not be re-rendered and your control not displayed.
As far as I see it, you have two choices
2) I've not worked with RichFaces (which is what I think you are using), but I think that if you add an "onchange" event to your input box, you might get your desired result. At the moment it looks like that it is the combo that will fire the submit event, but as tht isn't displayed there's no way to change it.