Yes you can do this. There is no need to "click" the mouse. Actions like "mouseover" or "mouseout" work just as well.
What you need to use is a <div> tag. Layout the page using <div> tags and then associate the mouse behavior with the position that the mouse is on the page.
If you use Dreamweaver there is a very good Tutorial in the Help files.
If the above does not help then come back to this Forum and I will provide you with some more guidance.
The important thing is that what you want to do is achievable.