This is the solution I used.
Copied and renamed vbulletin_core.js.
Modified popupbody so it handled mouseover and mouseout. Thus it has a delay in closing the dropdown for those that mouseout of the box.
Copied default popupbody function, renamed and changed the selector that is being detected. Use this for the accordion menus in the user control panel. You have to modify the user control panel template and replace the popupbody selector with the new selector obviously.
For tablets and other touch devices. I do feature detection for "touch" and conditionally load the default vbulletin_core.js or the modified vbulletin_core.js. I also added this piece of javascript from google as a touch screen helper
https://developers.google.com/mobile...s/fast_buttons. Solved almost all of that double click annoyance.
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I understand that not everyone can modifiy the javascript so you could just expand this jquery code and add a quick mouseout event with delay (650ms works for me), and accomplish the same thing.
Anyway my point is that you can just change the detected selector in the templates that triggers the javascript or jquery. That should solve your problem. Unfortunately, I cannot post the source of the javascript, that would be in violation of vbulletin copyright rules. (At least I think it is...). But if you are going down this route I will try to give you a hand, if you have a question.