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.

 

There are two JavaScript error messages in the console that provide a hint:

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

 

So, yes ... I know there's no API for this, but I am well proficient with JavaScript to code things, if I just knew what, if anything, needs to be called, and with what parameter.