Force SSL Exclusively enabled, HTTPS page elements not all secure

If I enable “Force SSL Exclusively”, my shop page shows “unsecure” resources, in my case “Search” form on the page is returning the calls over http (not https as it should).
If “Force SSL Exclusively” is NOT turned on, everything works on SSL pages as it should.

The problem is that I would like my page to switch to http when not in the shop area of the page & of course to work fully secure when in the shop area. Looks like this plugin does not work as promoted. Any ideas??

https://wordpress.org/plugins/wordpress-https/