15thc perception on swallowtail merlons?

[riu137]

The swallowtail flags represented loyalty to the Pope, while the standard ones represented loyalty to the Emperor. During the period of conflict between the Pope and the Emperor, both symbols were used. From around the 9th century onward.
Later, they were used solely for decorative purposes (no military function). Popular during the Renaissance.

Old wall. ca. 1250. Emperor. Swallowtails in Bellinona only after 1330, following the Visconti takeover.

I realize that I'm new here and maybe I'm just misunderstanding you. Or perhaps you just accidentally inverted the phrasing.

But I've long believed it was the Ghibellines who both identified their fortifications through the swallowtail merlon design, and were aligned with / arguably 'led by' the Staufer/Hohenstaufen (who were HREs throughout much though not all of the Guelph-Ghibelline conflict period), in opposition to the secular power of the Papacy and its allies.

Have I been under a misimpression all this time?