Request for a minimal search plugin

I cannot find a plugin or code that will do what I want and it is the most simple thing. Maybe someone would like to make this plugin?

What I am looking for is a plugin that utilizes Google Custom Search located at http://www.google.com/cse/manage/all wher you enter your “Search engine unique ID” and Google API.

What I am looking for is a small and minimal rectangle field to enter your search with no add ons, hyperlinks, advertisements not even a submit button. Just small so it takes up little space in a sidebar for instance. Maybe there could be a default word like “search” or “search this site” in the entry box until you type something in.

Google has a gadget that works for this but it has all the ads, google plus, hyperlinks etc making it way too large.

If someone could make this I think it would be a big hit! I’m just sayin’