Touchscreen get browser click or ouse even type

We have an Elo touchscreen that has multi touch. This can be probably for most touch screens as well, but we are trying to capture the “event type” on the body when a user touches the screen so we can trigger a timeout event. Right now we are using jQuery just for ease.

$('body').on("click mouseover mousedown touchstart touchend mouseup", function(e){
   console.log("trigger type" + e.type);  
 });

Is there a way with Javascript (or jQuery) to get the touch type without first defining the events we want to watch for?
Instead of having to define and watching, setting a case statement, etc for “click”, “mousedown”, etc.
Is there a way to just get the event type?

My assumption is probably not, but since it is a proprietary touchscreen manufacturer, knowing the type from the DOM would be helpful. We are using Chrome/Chromium for a web app interactive for this.