I think you misunderstood the question.
I want the box around the text and the drop down arrow to always be visible, not just when someone mouses over it. The functionality of DropDownExtender is ass backwards.... It only displays the box and arrow when you hover over the text, how is anyone supposed to know that there is functionality there?
My current work around was copying all the HTML generated by the DropDownExtender which is displayed during hover and placed it around the ASP.NET label, but that is the wrong way to go about doing it....
DropDownExtender should have a DisplayMode = Hover or Always... not for the panel or control it displays when clicked, but for indication that there is something to click on.
This functionality I cannot find, whether I look through the code or the documentation or these forums....