It keeps the clock up-to-date, but I use Konsole's "monitor for activity" feature, which changes the colour of inactive tabs if there is output.

Instead, this seems to work:

  TRAPDEBUG() {
    case "$WIDGET" in
      zle-line-finish)
        zle reset-prompt
        ;;
      *)
        ;;
    esac
  }

(I don't know if further cases will be required.)

This updates the prompt after "enter" is pressed, but before the command is executed.