Please see this KB article to learn how the new Search Bar features work. https://support.mozilla.org/en-US/kb/search-bar-add-change-manage-search-engines-firefox

The main thing that threw me off, was that you need to type at least one letter for a search in the Search Bar to see the drop-down that used to open when you clicked on the search icon mini-image in the search bar.

You can revert to the old scheme like this. Open up about:config (typed in the Location Bar) and toggle this preference to false browser.search.showOneOffButtons Then restart Firefox.

Thanks! That solved the mystery.

You can add a dropmarker to the search bar just like you see at the far at the right end of the location bar with code in the userChrome.css file.

Add code to the userChrome.css file below the default @namespace line.

• http://kb.mozillazine.org/userChrome.css

@namespace url("http://www.mozilla.org/keymaster/gatekeeper/there.is.only.xul"); /* only needed once */

/* search bar */
#searchbar .autocomplete-history-dropmarker {
 -moz-binding: url("chrome://global/content/bindings/autocomplete.xml#history-dropmarker");
 display:-moz-box !important;
 -moz-appearance: toolbarbutton-dropdown !important;
}

The customization files userChrome.css (user interface) and userContent.css (websites) are located in the chrome folder in the Firefox profile folder.

• http://kb.mozillazine.org/Editing_configuration

• Create the chrome folder (lowercase) in the <xxxxxxxx>.default profile folder if this folder doesn't exist
• Use a plain text editor like Notepad to create a (new) userChrome.css file in the chrome folder (file name is case sensitive)
• Paste the code in the userChrome.css file in the editor window
• Make sure that the userChrome.css file starts with the default @namespace line
• Make sure that you select "All files" and not "Text files" when you save the file via "Save file as" in the text editor as userChrome.css.
  Otherwise Windows may add a hidden .txt file extension and you end up with a not working userChrome.css.txt file