Harris's point is that there are only speech centres on one side of the brain. Both hemispheres have sensory and motor cortices and control of half the body, so the sense in which the right hemisphere is silenced/held prisoner is that it can't generate or understand speech.

If "you" are setting out to converse with the neighbouring regions of your brain, which in my experience is a worthwhile endeavour that does pay off, it'll have to be through visualisations, symbols, images, daydreams, imaginings.

Like any adult language-learning, there are a bunch of practice exercises before you're ready to converse in vivo. As a way in for you: first get a bunch of spare attention through your meditative practice. Then use it to work on visualisation of familiar places like your house/neighbourhood until you can move around fluently. Repeat with a request like "find something red" and notice when a part separate from your monologue locates it without effort/searching. Then start making broader requests for imaginary landscapes or situations and see what replies you get. Be a kind, accepting, fearless conversation partner. Look for surprise and speed as markers of authentic responses from elsewhere than your monologue.