I posit that the human mind is made up of dozens, or perhaps even hundreds/thousands "smaller agents" that work together to create consciousness as an emergent property of the whole, which makes it impossible to isolate and say "this, THIS right here IS concsciousness".
That does not mean each of those has their own personality, per sé.
IIRC the "other consciousness" is the internal monologue or internal visualization you experience when thinking
There's a potentially related theory too that the origin of religion is internal narrator thinkers having perceived the internal narrator as a second entity who was issuing them commands and beliefs rather than their own internal dialogue.
These people would claim to be "prophets" and basically evangelize whatever presence they ascribed responsibility for the internal narrator to. Leading to more people believing their internal narrators are also these divine forces speaking to them.
Not to dunk on rural americans, but a phenomena like this could also explain the recent evangelical movement in the US considering how much emphasis is placed on the personal relationship and communication with God, these people might actually just not realize their own thoughts and ascribe all thought process as the voice of the big man himself.
I will always held belief that we are part of the spiritual greater universe and our brains are antennas for the consciousness. At the same time I won’t allow this belief to interfere with my daily logic and scientific pursuits.
It’s way more fun to have some nice private things you are contemplating as you enjoy the various psychedelics.
As far as I understand, the line gets even blurrier then that. Apparently quiet a lot of the subsections of your brain do things that can be interpreted as conciseness, but we experience it as one unified thing.
The only thing I can think of that this could refer to is split brain patients who have undergone a specific medial procedure once used to treat epilepsy. It's possible, although not well understood, that the two halves of their brain operate sort of independently, and only one has access to speech.
It's a very interesting topic, well worth diving into! But it's also very muddy, there is contrasting evidence for and against the "two mind" theory.
Anyway, I'm fairly certain this "theory" does not apply to healthy brains which have not undergone this procedure.