Question

I need this structure to organize my code…so that I can call it like this

Control.Menu

Here is my attempt:

var Control = 
{
    Menu : menu  
    {
        menu_timer:     0,
        menu_element:   0,

        top_mouse_over: function ( id ) 
        {
            Menu.bottom_mouse_over();
            Menu.menu_element = document.getElementById( id );
            Menu.menu_element.style.visibility = 'visible';
        },
...
    }
};

Answer 1

This is your problem:

Menu : menu  
{
    …

What’s the menu on the right side of the colon for? All you need is this:

Menu: {
    …

Inside top_mouse_over(), Menu won’t be defined:

Menu.bottom_mouse_over(); // This isn’t going to work

…it was just a property on the Control object; you never created a Menu variable anywhere. Instead, you can refer to it as Control.Menu, or use the this keyword. In a function, this is whatever object the function was called as a property of, i.e. the thing to the left of the dot. In this case, if you call it like this:

Control.Menu.top_mouse_over(someId);

…then inside top_mouse_over, this will point to Menu. You could change the body of the function to this:

top_mouse_over: function ( id ) 
{
    this.bottom_mouse_over();
    this.menu_element = document.getElementById( id );
    this.menu_element.style.visibility = 'visible';
}

(If you’re not familiar with this, please read up on it before you use it. Until you understand it, it will be easy to make mistakes.)

FWIW, common convention is to capitalize only constructors (functions you call with the new keyword), and to start anything else with a lowercase letter.