Is it possible to programmatically identify the **field** that is being used to Table Join two datasets together in ArcMap?  

One method I tried was looping through all of the fields and look for a matching "baseName", but that is just an "educated guess" where you are hoping that the fieldnames in both databases are the same.

For a graphic representation of what I am after, I basically want to  identify the "Input Join Field" and "Output Join Field" as seen in the "Add Join" dialog, but after-the-fact, of course.

![How to identify the "Input Join Field" and "Output Join Field"?][2]

This is a tag-on question to [Can a “Join” be detected programmatically?][1], but in this case I want to extend the functionality to identify the FIELD(s) being used to join the two (or more) datasets together.
  [1]: http://gis.stackexchange.com/questions/7703/can-a-join-be-detected-programmatically
  [2]: https://i.sstatic.net/9EzkM.jpg