footnotes in split colums line thickness

Here a screenshot from my German InDesign showing the Footnote Options > Layout tab:

As you can see Rule Above ( Linie über: ) has a dropdown for Continued Footnotes (Fortgesetzten Fußnoten). Same options are available with First Footnote In Column (Erste Fußnote in Spalte).

Regards,
Uwe Laubender

( ACP )

> ... or do I need to place a white frame to cover and set a textline whenever columns are split[?]

No, you need to read up on how to format footnote options 🙂

See the Online Help: https://helpx.adobe.com/indesign/using/footnotes.html#change_footnote_numbering_and_layout

Relevant quote:

Rule Above:

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.