Telepathy is fundamentally communication – a bridging of thoughts, a direct link between minds.
There is no single gene that controls telepathy. It is a synergistic effect that stems from a dozen or more genes. The strength of an individual's telepathy is similarly not directly linked to any single gene. The puzzle is further complicated by "mundane" genes – genes that have existed in humanity for millions of years but have new effects when acting in concert with the "new" telepathic genes.
The phenomenon that is telepathy exists primarily in hyperspace. Sentient consciousness is an informational construct in the intersection between hyperspace and realspace with the organic brain serving as an information processing device. The personality engram of every individual is encoded in an information matrix and inscribed into the very structure of space-time. In short, a portion of the mind – the pattern of information encoded in the structure of space-time that contains a person's unique personality exists in hyperspace and telepaths can access this information pattern.