I would say (I'm a 4w5) that the deep connection I long for is defined more in opposition to what I experience now. I am inherently aware of what I desire in relationships because I know what I find so unfulfilling in my present interactions. That deep connection I desire is not: fickle, superficial, difficult, over-complicated, selfish, empty, cruel, indifferent, critical, affected, dishonest, or disloyal (I could go on and on). I guess most people say they don't want these things but, for some reason, they don't seem to really mean it. Maybe the difference is my tolerance for these things is that much lower than for others. Maybe my heart is simply more unresponsive and is not as easily touched.
I guess the essential requirement for me to feel a 'connection' is that it should be so easy. I find most interaction with others (even if they are perfectly nice people) to be rather laboured, contrived and hollow - like the equivalent of a forced smile. I want to feel an immediate and deep affinity for another, combined with a spark of enthusiasm and avidity brought forth in myself - something to actually make me sit up, bringing me to life and driving me forward, pursuing further interaction. What does this feel like? It feels like I am actually alive; that a part of me has been awakened because I can really feel joy and fervour for another human being (and not merely art or nature etc). I guess this is a combination of both chemistry and compatibility because I really think its impossible for me to experience one without the other. The chemistry comes from the commonality (in the broadest sense: commonality in heart and mind, not purely interests). And the reverse is true: no commonality, no spark.