Automate double password confirmation typing by means of Greasemonkey

Ever seen, and really hated, one of these?

Password:
Again:

Wouldn't it be rather stylish to have a Greasemonkey script fill in the second entry as you type the first, when there was nothing written there in the first place? (Yes, it severely defeats the intended purpose of the double check, I know. But let's move on.)

A good solution to the above would look for any two password fields in any page, that do not have any other visible form widget between them, and attach an onkeypress handler to the first, passing on the event, or a copy of it, to the other field as well. Points of style for additionally verifying that they are not very far apart in the page flow using this, or some variant thereof:

function getScreenCoordinates( node )
{
  var x = node.offsetLeft;
  var y = node.offsetTop;
  while( (node = node.offsetParent) )
  {
    x += node.offsetLeft;
    y += node.offsetTop;
  }
  return { x:x, y:y };
}

The Google Reader blog mentioned a while ago how you synthesize your own mouse click events; I'm sure it's not far from how it's done with keyboard input. Their code looked like this:

function simulateClick( node )
{
  var event = node.ownerDocument.createEvent( 'MouseEvents' );

  event.initMouseEvent( 'click',
                        true, // can bubble
                        true, // cancellable
                        node.ownerDocument.defaultView,
                        1, // clicks
                        50, 50, // screen coordinates
                        50, 50, // client coordinates
                        false, false, false, false, // control/alt/shift/meta
                        0, // button,
                        node );

  node.dispatchEvent( event );
}