Can I attach a javascript function to a Drupal.behaviors javascript function?
Yes you can. You can attach as many event handlers to any DOM element as you want.

So you have to write your own module that alters the output (is a form? some form_alter function. Is a page? some ouptut alter function or theme function) adding your custom JavaScript. 

In your custom JavaScript add the code using behaviors that attachs your event handlers for the click event. 

The tricky part is how you locate the next and prev buttons. You can start from the code snippet you posted. It seems that prev and next buttons are located here:

 var multipageControl = new Drupal.multipageControl({
      title: $('&gt; .multipage-pane-title', this).text(),
      wrapper: $(this),
      has_next: $(this).next().length,
      has_previous: $(this).prev().length
    }); 


See the has_next and has_previous entries.

Looking at the previous lines you can see:

// Transform each div.multipage-pane into a multipage with controls.


It seems that the $(this) code referes to a div.multipage-pane, so the buttons seem to be:

$prev_buttons = jQuery('div.multipage-pane').prev();
$next_buttons = jQuery('div.multipage-pane').next();


Disclaimer: I don't know that module so I am shooting blindly but I think this approach will work.