To make this work with Toolbars throughout your app without having to put duplicate code everywhere a toolbar exists, I suggest going this route.
For Toolbars on forms/UI objects other than a VP, use this ...
Form (or whatever) > Advanced Scripts > Initialization Script
for (var i = 0; i < widgets.length; ++ i) {
if (widgets[i].type == "toolbar") {
widgets[i].config.click = openMenu();
}
}
For VP's use ...
Visual Perspective > Top Bar > Other Settings > Advanced > Initialization Script
config.click = openMenu();
For the logic that actually handles the button clicks and opens and closes a given menu, put this function in a custom js file, so that it can be called from anywhere in the app.
Custom JavaScript File
function openMenu () {
return function(e) {
var element = e.target.closest(".k-split-button") ;
var popup = element.data("kendoPopup");
if (popup) {
if (popup.visible()) {
popup.close();
} else {
popup.open();
}
}
}
}