To find it let us look at one of the most essential requirements for consciousness; it is an undisturbed heart pulse which is without question a necessity for consciousness. Because neurone firing is robust against small disturbances like this, we may conclude that the blood pulsation is a fundamental component in the non-neuronal network. Therefore, we can conclude that there must be a system which depends strongly on blood flow dynamics without directly influenced by neurone processing.
So far, we are now looking for a non-neuronal computation network which strongly depends on blood pulsation.  and which mechanisms could have been overseen by neuroscientist for all the years?Why has it overlooked since now. One reason could be, that the brain must be conscious, which in many experimental set-ups wouldn’t be the case. The other reason could be that the computation is based on quantum mechanics which cognitive neuroscience, defined in the realms of classical physics, wouldn’t observe.
This possibly is supported by results in quantum cognition where is has been shown that the mathematical formalism of quantum theory can be adopted to model cognition showing advances over traditional classical probability theory in many aspects of cognition. 
Summarizing, we can say that a computational network should exist in the brain with the following properties; (a) non-neuronal, (b) based on blood dynamics, (c) quantum processing and (d) spatial and temporal properties different from neuronal network.