Event listener for when element becomes visible?

Going forward, the new HTML Intersection Observer API is the thing you're looking for. It allows you to configure a callback that is called whenever one element, called the target, intersects either the device viewport or a specified element. It's available in latest versions of Chrome, Firefox and Edge. See https://developer.mozilla.org/en-US/docs/Web/API/Intersection_Observer_API for more info.

Simple code example for observing display:none switching:

// Start observing visbility of element. On change, the
//   the callback is called with Boolean visibility as
//   argument:

function respondToVisibility(element, callback) {
  var options = {
    root: document.documentElement,
  };

  var observer = new IntersectionObserver((entries, observer) => {
    entries.forEach(entry => {
      callback(entry.intersectionRatio > 0);
    });
  }, options);

  observer.observe(element);
}

In action: https://jsfiddle.net/elmarj/u35tez5n/5/

var targetNode = document.getElementById('elementId');
var observer = new MutationObserver(function(){
    if(targetNode.style.display != 'none'){
        // doSomething
    }
});
observer.observe(targetNode, { attributes: true, childList: true });

I might be a little late, but you could just use the MutationObserver to observe any changes on the desired element. If any change occurs, you'll just have to check if the element is displayed.