Twitter bootstrap dropdown show/hide events how do they work - twitter-bootstrap-3

Question

I am trying to understand how the show/hide logic of a dropdown in twitter bootstrap works.
I can declare a dropdown menu in a navbar purely with HTML, and yet it seems that Javascript is involved with showing/hiding the dropdown. Also the dropdown disappears if I focus out by clicking on an unrelated area on the page.
Question part 1: Where can I find the Javascript code that is involved with Dropdowns in bootstrap?
Question part 2: Is it somehow possible to tap into the event logic and execute some custom Javascript code when a certain dropdown receives a focus out event? For example so that I can hide another (unrelated) element on the page when the dropdown looses focus?
To be more precise:
Lets say I declare a bootstrap dropdown purely in HTML (this would be inside a ul.nav.navbar-nav):
<li role="presentation" class="dropdown">
<a id="mainmenu" class="dropdown-toggle" data-toggle="dropdown"
role="button" aria-haspopup="true" aria-expanded="false">
Lectures <span class="caret"></span>
</a>
<ul class="dropdown-menu">
<li>Action</li>
</ul>
</li>
Now somewhere else on the page I have the following HTML:
<div id="#background" style="display: none">
<img src="...">
</div>
When I click on the dropdown button bootstrap will show the dropdown, but want two additional things to happen:
The div#background should be shown
Assuming I click somewhere outside the dropdown (which will cause bootstrap to close it), I want the div#background to be hidden again.
I think it should somehow be possible to register my own callback function on some bootstrap event and show/hide my div from that callback, like so:
/* just to illustrate my idea */
hide = function(element) {
element.style.display = "none"
}
show = function(element) {
element.style.display = "block"
}
}
So how and where could I register the hide and show functions such that they get called when I open/close the dropdown and also when I click on an unrelated area on the screen, which will cause the dropdown to close.
If this is possible to achieve purely in HTML by attaching some data-* elements to my div#background then I would like to know about that too.

Answer 1

First:
Do you think about something like this?
$('.dropdown-toggle').dropdown();
Got it from w3schools.com
Second:
You can do call the dropdown link
$('#element').click( function(){
$('#dropdownElement').dropdown();
});
Is that what you are looking for?