The Instant Find Next command doesn't have a button on the search toolbar because it doesn't use the search term you've entered on the search panel or any of the search options. It is listed in the Search menu, primarily so you can assign it a keyboard shortcut in the Keyboard Preferences. The default shortcut is Ctrl+Alt+H, which is the most instant way of doing an Instant Highlight. If you turn on the "double-clicking a word instantly highlights all occurrences of that word" search preference, then double-clicking a word also turns on Instant Highlight.
Select Instant Highlight in the Search menu to highlight all occurrences of the selected text or the word under the cursor, without using the search toolbar or panel. Occurrences of the word as part of longer words are also highlighted. Differences in case are ignored. Highlighting persists when you switch between files. All search options, including Case Sensitive, Whole Words Only, and All Files, are ignored.
Use Instant Highlight with the same selection or on the same word to turn it off. Only one search term can be highlighted at any time. If you use both Highlight All and Instant Highlight, using either command turns off the other.
Search|Instant Find Next
Search|Instant Find Previous