There is onAfterEventRender event that you can use to attach custom listeners to the event div:
https://api.daypilot.org/daypilot-scheduler-onaftereventrender/
Example
dp.onAfterEventRender = function(args) {
args.div.addEventListener("mousedown", function(ev) { ... }, false);
};
Just note that some events are handled by DayPilot and adding a custom event handler may disrupt the built-in functionality.