If we guess from the animal's character and behavior, mice and rabbits are relatively timid and may talk to themselves because of fear. But this speculation has no scientific basis.
If we guess from the characteristics of the zodiac, talking to oneself may refer to a snake, because the snake is the only animal in the zodiac with no feet, so it can't communicate with people and can only talk to itself. But this is just a humorous guess, and there is no actual basis.
In a word, soliloquy is a kind of human behavior, which can't directly correspond to the zodiac.