A boilerplate static demo of clicking a logo and having a search form submit that particular logo name.
Click on an image below, and it will fill in the 'name' of that logo and run a search at: https://showmeweights.com. Keep in mind that you will just have to observe this from dev tools, as the query cannot be submitted from an external site.
However, a similar principle could be applied and should work if the search query is run on the same site...theoretically.</