When the player who is not the owner of the rebellious piece moves it, we waste quite a few words describing this event -- so from now on let's define a "rebel move" as the move that is made by a rebellious piece when the owner is not the player on the move.
I thought of dozens of different rules for rebellious pieces, and for games with rebellious pieces, and chose two. In both games, I used the same rules for the "Rebel Move".
"The Rebel Move must be one square, forwards or sideways, not a capture, and not to a square to which the owner could move the piece." This means pawns can only move sideways, Kings and Queens cannot be rebellious (against whom would they rebel?), and we don't have to make a special rule saying it's illegal to undo the opponent's move (because you can't! It's much simpler that way.).
In addition, the rule as stated defines the Rebel Moves of the fbNF, WD, Berolina Pawn, and anything else you care to name. Notice that the Q cannot be rebellious, but the RN can -- therefore playing Chess with Different Armies using rebellion rules is a bit iffy, although of course you can play Squirm Chess in which both sides use the Clobberers instead of the FIDE army.
So here are the two games, with their long and complicated rules:
A few points, though: in Progressive Squirm Chess, only the last piece that moved is squirmy, even if the opponent moved ten different pieces. It's okay to put yourself in check when you squirm the enemy's piece, because you still have your normal move. If you can put the foe in check with a squirm, his move was illegal.
In Rebellion Chess, both players will soon have really awful Pawn formations, and each player will have 2 Bishops of the same color -- or 2 FAD and two BD of the same color! (The Nutty Knights probably have an advantage in this game.) The midgame is a picture of frustration, as you struggle to get your pieces into decent positions, but then the anguish is rewarded by triumph as a piece or two finally breaks free and amnages to attack the enemy -- some people will like this game, and others will absolutely hate it!
Rebellion Chess begs to be played with Berolian Pawns.
Both games have been playtested a bit. I expect that Squirm Chess will be more popular, if nothing else because of the intriguing mental image of the piece squirming out of your hand and winding up on some other square than where you intended.
I also rejected Avalanche-style rebellion, in which you'd make one normal move and one rebel move. No good reason for rejection, it's probably a good game.
The idea of a rebellious piece, which is in effect a semi-neutral piece, seems to me to be an entirely new concept in Chess Variants. It is unlikely that I have found the best and most playable game to express this idea (although I do think these are good). Feel free to beat me at my own game!