Mouseover Search Box on Navigation Bar

Hi – I’m using a twentytwelve child theme and would like to include the text “Search” as a menu item. I would then like to be able to mouseover the word “Search” and have the Search Box appear.

I was able to add the searchbox to the navigation bar, but I can’t seem to figure how to use just the text and have the Search Box pop up on the mouseover.

Here are a couple of examples if you scroll over the Search menu items on these pages to see what I am trying to do.

https://www.tallandsmallphotography.com/
https://www.elisabethmillay.com/

Thanks in advance for the help!