There is a technique that will at least allow you to be the first in line (unless another script employs the same trick - unlikely).
What you have to do is hijack the click event. This related question demonstrates the technique: Hijacking onchange event without interfering with original function
All we do is redefine the click
function to be one of our own choosing, e.g.
var myButton = document.getElementById('button1')
var oldClick = myButton.click;
myButton.click = function(evt) {
//do whatever you want. When done, call the default click function:
if (oldClick) oldClick(evt);
}
(the syntax in the linked question is superior, but the above code is easier to read).