Thought has been conclusively resolved to come from the brain, how exactly it does this is still uncertain but it is widely agreed upon that thought originates from the brain. So, if you have a separate consciousness it's either a 'switch' of an original consciousness in the brain OR it's a parallel consciousness (the former would mean you can be either/or consciousnesses, the latter suggests you can be both characters at the same time). This would be interesting, but ultimately is an abnormality in the brain usually likened to some form of psychotic disorder, such as schizophrenia (I'm not meaning to offend at all, I'm just saying the classifications).
Now the question is, is the proposed separate consciousness a true separate consciousness or a 'lesser' second consciousness. The former suggests that your body can be controlled by the second consciousness just as well as the first, that both consciousnesses are interchangeable and there is no real 'primary' person but you are multiple people in the same body. You don't know the feelings and possibly memories of the second consciousness and the second consciousness doesn't know the feelings of the first (Neither consciousness has any control on each other). 'You' could be equally and correctly defined as either consciousness, no one consciousness is 'primary' and 'alternate' but all consciousnesses in your head are equal. As in, there is no "character", you are as much of a "character" as that "character" is to you. This is likened usually to multiple-personality disorder. The latter suggests you have some form of control over the second consciousness and the second consciousness usually influences the primary, but don't exist as separate characters. IE: You exist and the second consciousness doesn't, you may still not have much control over the second consciousness but it simply influences you indirectly, in reality it's a formation of the primary consciousness. That is, you created the secondary consciousness, willingly or not (as opposed to both existing independently in the previous scenario). SO that would be more defined as schizophrenia.
It sounds like you're referring to the second in which case it's unlikely it has a mind of it's own, but it's "mind" is simply a creation of your consciousness that is affected by unconscious parameters (maybe malfunctions) in the brain. It doesn't really exist, but it's more just a hologram of something that does.
Just thought I'd ramble on a bit xD