Top navigation search section has two tab indexes

When navigating with keyboard – tabs on the top menu, the search field has two entries, one of which is not visible unless interacted with.

This second entry should only be displayed when the 'search' section is toggled on.

It's by default collapsed for visual users, it should be collapsed semantically too.

Expected behavior:

Only one tabbing order, assigned to the search button which is visible.

Example:

Made with Firefox accessibility tools, see 5 and 6: