In Word 2003, the button you mention should be on the Header and Footer toolbar. If you can't see the toolbar, select it from View | Toolbars when you have activated the header/footer view. Or you could add the button back to the toolbar via Tools | Customize, if it is just missing.

Also, the button have different labels in different versions of Word: Same as Previous or Link to Previous.

For what it's worth, Word automatically creates section breaks for you when you change section-specific formatting (such as page setup or columns) for the selected text; this is true for all versions (going back at least to Word 97).

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Stefan Blom
Microsoft Word MVP

Microsoft 365 apps for business
Windows 11 Professional