在自定义控件中使用浏览器的本地下拉图像/图标

I'm looking to implement a true combobox. Users can enter text like an input and also click a drop down icon and select a value that way. I did a quick search and didn't find any pre-existing library I could use for this. All the ones I found, seem to just be an extension of jQuery's autocomplete where you have to enter a value that is in the autocomplete drop down, but I can't have that restriction. So I was going to roll my own. combobox. Users