4 Clone concepts and how Clones relate to Mutual Majority

I see at least 4 different clone concepts:

candidates that are ranked equal on all ballots (Approval and Mean Ratings satisfy that unlike the next criterion):
candidates that are ranked together on all ballots (Tideman Clones, the typical meaning of clones)
candidate that are ranked equal on more than half the ballots
candidates that are ranked together on more than half the ballots

Satisfying the 2nd and allowing equal rankings means that the 1st is also satisfied. Satifying the 4th and allowing equal rankings means that the 1st, 2nd and 3rd are also satisfied.

James G-A asked somewhere on the electorama list whether satisfying independence of Tideman Clones and First Place Majority together means satisfaction of the Mutual Majority criterion. Well, these things are somehow related but not like that. Here is a method that satisfies Tideman Clones and First Place Majority, but not Mutual Majority (for demonstration purposes only):

Take the option that gets more than 50% first pref wins if it exists, else scan the ballots for Tideman Clones to make the selection Tideman Clone independent and elect the Borda winner from that set.

I think an option satisfies Mutual Majority if it satisfies First Place Majority AND is independent of options that are regarded as Tideman Clones by more than half the ballots (clone concept 4).