I just had to hack a bit of code in dijit.Menu.js to make it record the DOM node clicked by the user to open the Menu, so I thought it could be nice if Dojo had this functionality included in next revisions.
All I changed were 2 lines, that I added to function _openMyself, circa lines 239 and 245:
var self=this;
self.targetNode = e.target; // <--- Added this line
var savedFocus = dijit.getFocus(this);
function closeAndRestoreFocus(){
// user has clicked on a menu or popup
dijit.focus(savedFocus);
dijit.popup.close(self);
self.targetNode = null; // <--- Added this line
}
self.targetNode = e.target; // <--- Added this line
var savedFocus = dijit.getFocus(this);
function closeAndRestoreFocus(){
// user has clicked on a menu or popup
dijit.focus(savedFocus);
dijit.popup.close(self);
self.targetNode = null; // <--- Added this line
}
That allows me to programmatically find out which DOM Node the user clicked to open up the menu, like this:
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.
.
function onMenuOpenHandler() {
var tgt = this.targetNode; // <--- This is the DOM Node the user clicked!
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.
.
.
.
function onMenuOpenHandler() {
var tgt = this.targetNode; // <--- This is the DOM Node the user clicked!
.
.
.
Cheers

ER
You could file and enhancement request in trac.dojotoolkit.org, although you should sign the cla and attach a patch to the bug after filing it. Thanks.