What version of Pega is this? From the markup, I see that the menus here are the old generation menus. Depending upon which release you are in, you might have an option of upgrading menus from the HTML5 readiness landing page.
I am wondering why you would want to trigger click on the menu items programatically, can you not just call the action configured on the menu item directly instead.
However, if you still need to trigger click, try this: