So essentially I'm attempting to add ClassName to some Home link in navigation bar on the top of page.

How to locate this PHP producing code? Example appreciated.

Many thank you.

I dont think its likely to include custom class to menu produced by wp_nav_menu function right now.

However you may create a custom Menu @ Dashboard > Appearance > Menu and hang it as being Primary Menu.

And then add the "Home" link as custom food selection, which will generate unique id for home link and each one of the food selection from the format "menu-item-<menu_item_id>" and classes from the format "menu-item menu-item-type-custom menu-item-object-custom [current-menu-item] [current_page_item] menu-item-home menu-item-<menu_item_id>".

(<menu_item_id> - is a few no. and sophistication within [ ] is optional.)

You should use the id or among the classes or both, to complete what you would like using the CSS or javascript.