Search Settings Icon Only Not Available

I would like my search form to just have the icon (Dropdown style), but that option doesn’t seem to be available on my end.

I tried following this:

Change Menu Search Form Style

However that is not available. When I click on Settings, “Form Style” does not exist.

When I go to Design > Search Form Customizer > I only see the options with the input box.
Screen shot attached of waht I see available.