Scaling additional item in header

I read the post…
https://kriesi.at/support/topic/shrink-additonal-content-in-shrinking-header/
… and spent considerable time trying to get this to work for my site, but without success.

My questions are…
– what new styles to create?
– do I need to edit includes/helper-main-menu.php at all?
– in a child theme what is the specific syntax of the functions.php file (which I would create for this)?

Thank you