Specify the location and appearance of the footnote divider line that appears above the footnote text. A divider line (also called a “separator line”) also appears above any footnote text continued in a separate frame. The options you select apply to either the First Footnote In Column or Continued Footnotes, whichever is selected in the menu. These options are similar to those that appear when you specify a paragraph rule. If you want to remove the footnote divider line, deselect Rule On. (my underlining)
So contrary to what you say in your first line, you can format the "Continued" line -- it doesn't need a script either.