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.
Do you have any further reading or information on communicating with the other hemisphere?
It has helped me attain the deepest level of meditative state, where I am almost aware of my consciousness as a separate process from the constant sensory input. Becoming an observer, empty-head.
On another level, I've found it very settling in times of emotional turmoil.
I did have a near panic attack from the book when he makes somewhat of a case that both hemispheres of our brains might be independently conscious, with one permanently silenced as control of the body is held by the active one that controls our body. A prisoner in someone else's body, literally, with no way to interact with the world. It is pure physiological horror. But alas I cannot do anything about (other than try to talk to that other entity and see if it can trigger some sort of response?) so no use getting worked up? The world is full of day-to-day cruelty and it's not my fault.