When I first started trying to shift my focus to my right brain (in the first weeks of this experiment), it felt a little disorienting. I was so used to identifying myself through my left brain (where the ego resides): a constant commentary running through my mind - discussing, comparing, judging, reminding me of things I need to do.
When I would consciously try and shift to my right brain (by literally imagining it - focusing my attention on the right side of my head), I would get a slight headache. It felt like a weak muscle needing to strengthened.
Another specific way to practice this is to shift your visual field from a narrow focus on specific objects in your field of view, to a "wide lens" field of view (peripheral vision). I recommend trying this while in motion, such as walking, and not just in a sitting position or during meditation. This exercise quiets the left brain, and activates the right brain - and is particularly helpful in making a quick shift during high activity, when the left brain would normally be dominant.
As I did this regularly throughout my day, it felt odd. I felt kind of "blank" in my mind. Instead of feeling good, my left brain immediately put its judgement on it to try and gain control back. It would say things like, "this is boring, maybe I'm depressed, I won't be effective if I have a quiet mind, YOU NEED ME!!"
So right now it's about practice and noticing - lots of practice and noticing, so that the ability to consciously "switch platforms" becomes strengthened.