When I'm tired I sometimes get an inner monologue that just keeps going, but it's nonsensical, like a Markov chain. I have to actively stop it. Annoying.
I get this too! I have to be really tired, lying down and calm. I always think of it as listening to the noise of my subconscious. Mine isn't continuous, more I can pick up nonsensical phrases every 10-20 seconds. I've never heard of anyone else having this!
Have you tried voicing it out loud and recording yourself?