>>24645984 (OP)
The Judge is the brains capacity for pure reason applied to the self. In the way the novel conceptualises mankind, on some level everyone knows they're evil, or would be if they had different incentives, that's what your capacity for reason figures out about yourself in the first instance. But people don't like to believe this, so this knowledge gets repressed and sublimated, laundered and papered over and from that you get the illusion and inconsistent practice of morality in daily life. The Judge is haunting because he's meant to represent the natural conclusion you would come to, being as smart as you are, that you have had to forget and work to unknow. He's your reason alone judging you.
Early in the book the conversation the kid has with the hermit reflects this. The mind can't fully know the mind, because it only has the mind to know it with. But the mind can in theory know the heart, but it doesn't want to, and you shouldn't try to know it. The Judge is the mind knowing the heart. That knowledge is never going away, always dancing on over and back around the edge of conscious perception, never dying and promising ultimate doom to all of our efforts to distance ourselves from the state of nature and the spoiling the belief that we can be in some way saved.