I installed Debian 13 Trixie RC2 and selected Cinnamon during installation. I encountered the same problem as described and tested both the “When printers exist” and “When printing” options. In both cases, the icon remained visible and did not respond to click or double-click actions.
After some investigation, I found that the issue was caused by /usr/bin/lpq not being installed. Once I installed the cups-bsd package (which provides that tool) and re-added the applet, the problem disappeared. Hope this helps.

