Select2 for jQuery is some sort of type-in-a-select-list-to-search-for-something widget.

I'm not sure if this or this is where to get it. It's worth a look. It's pretty mindblowing.

 
 

Addendum 9/7/2017: One thing that can really sabotage these controls is to mismap the values for the ids for the dropdown selections. If the mapping is bad and all of the hidden values just end up undefined, you will not be able to make a selection or see any hover over highlighting when you mouse over results returned from a search.