In The Master and his Emissary
, Iain McGilchrist cites research into the neurological substrate involved when we gaze with
someone. When we attend to an object we re-cognise it in the left hemisphere. However,
When we shift our gaze where we see another looking, we do so via the right hemisphere. In humans, mutual gaze ... (i.e. when two people are mutually aware of their common attention to the same object), is accompanied by activation of a highly distributed network extending throughout the right hemisphere. .. In fact, shared mental states in general activate the right hemisphere. (p.168)
David Grove emphasised that when working with a client's metaphor landscape the facilitator should gaze (with their external or internal 'eyes') to the location of the symbol that was being addressed by a clean question. 
Mutual metaphorical gaze should have two effects:
Throughout the facilitator's right hemisphere a highly distributed network will be activated;
And, since the client knows that the facilitator is sharing their physical and metaphorical 'gaze' they too will have a highly distributed network extending throughout their right hemisphere activated.
So what, you might ask?
Well, to start with, sharing a mutual gaze to a client's internal landscape is not common in coaching/therapy sessions (where eye-to-eye contact is the norm) and if nothing else, the neuroscience says the client and
facilitator will be in unusual states. That alone has to increase the chances of something new happening.
And, according to McGilchrist, the left and right hemispheres have a "profound asymmetry" and are "fundamentally incompatible" in the way they experience the world, so much so that he says they have different worldviews. 
Because the left hemisphere is the seat of most kinds of recognition (except faces), it is preeminent when it comes to using existing
mental models. Therein lies the challenge of all change work. How does a person loosen their grip on their existing models long enough to allow a new model to emerge? Interestingly, 'seeing' something as whole and connecting with it's nature (rather than its parts and how they work) is the provenance of the right
Do you see where I am going?
If mutual gaze activates "a highly distributed network extending throughout the right hemisphere" then my guess is it will prepare both
client and facilitator to 'see' the big picture, the systemic, the betweenness, the reciprocal – and to go beyond the known; to notice something new, .NOTES
1 It's the same for other nonverbals such as voice direction and gesture. Penny Tompkins and I have summed this upby saying: the facilitator should make their nonverbals congruent with the location of symbols in the client's metaphor landscape - from the client’s perspective.
2 I'll have more to say on this in a later blog. Suffice to say here that McGilchrist is at pains to emphasise that it is more complicated, and infinitely more interesting, than the simplistic left-brain, right-brain split that was in vogue a few years ago.