Well, I know the properties dialog uses Tag.php with a parameter for which tag we are editing (... /Dialogs/Tag.php?Tag=TD ...). Opening the URL directly, obviously doesn't work, as it doesn't know which element is being edited, or the calling window.
Dialog_TagHead.js needs a parameter "arg"
Dialog_Tag_Td.js (in this case, presumably a different JS file if a different tag is being referenced) needs parameter "element".
For "arg", it gets its values from:
The function Window_FindDialogArguments is defined in Dialog_TagHead.js