This plugin will make your header image clickable. Header Image Clickable plugin adds two options inside header image section of customize. first is for header image link and second is for link target. if the header image is not set then both settings will be hidden so make sure, you have set header image.
Header Image Link: it will be link of header image.
Link Target: it is a check box input filed. if it is checked, link will open in new tab / window otherwise in the same tab / window.
Working: it extend the HTML of header image generated by the core WordPress. simply it adds html anchor tag for the header image.