Well isn’t this interesting? I’ll jump in on this and add a few thoughts about the rules of the game.
Firstly, there are not many limitations to the witch pieces, so some should definitely be added. I think it should be a rule that witch pieces can be made visible by certain moves on the board. So, let’s say that when a witch piece is invisible it’ll be called a Red Witch (based on the red truth) and when a witch piece becomes visible it’ll be called a Blue Witch (based on the blue truth). Since you mentioned pawns, it can be made that when a red Witch piece is straight ahead of a pawn, it becomes a blue Witch, thus Witches should try to avoid pawns. Also, when a pawn reveals a Red Witch, the pawn is taken by the blue Witch after revealing it. The King that is the most important piece should also be able to reveal red Witches, though the Witches are taken if the King reveals them, so they can’t get very close to the King either.
There also should be some way on how red Witches still stay invisible after taking a certain piece, cause then if they are still red Witches, the other player will know that they are on the square of the piece they just took. So maybe red Witches should get another extra move after taking a piece, but only a one or two square diagonal move so the opposing player knows that they are close by the square of the taken piece, but not their exact location.
As for how their turns should be, they should move in the regular manner, meaning that you can use them like every other piece, on your turn only and they are the only piece you can move on your turn, and you have to say that you moved a witch piece, which will make your darling opponent think well before moving their pieces. Also the whole ‘buying witches with points’ rule should be removed, four witch pieces should be given to both players at the beginning of the game like any other piece.
This is everything I can think of for now, let’s see your replies now.