I have a worse problem than having unspoken thought processes: some of my best thought processes are simply beneath the level of consciousness and I don't notice them at all until they're finished. Even then, I often get only an answer and not an explanation out of them. Surely this happens to everyone: the problem solved during sleep, the idea on a walk in the woods, the conviction that a conjecture is true on utterly minimal evidence, the argument that pops up full formed in the middle of a conversation.
My mathematical process is roughly this: consciously, I try a lot of stupid things which essentially have no chance of working but do have the benefit of exposing me to lots of examples; these examples pile up and are subconsciously masticated for days, weeks, months -- I'm not old enough mathematically to put "years" here yet -- and eventually by some inner and unobservable process I just have a feeling about what to do.
Perhaps that's an exaggeration. But I certainly do feel that way sometimes, and to the extent that it's true, it means that the whole project of trying to communicate how I thought of something is just telling stories, at least if I say anything other than "well, I just knew one day."