I get feelings like this, and frequently. In fact, if I don't get some sort of feeling that you've described for a while, then I begin to feel very empty, restless, and lost. I kind of need that -- it fuels my dreams, and I'm not much without those, to tell the truth.
The year I spent in the Netherlands, I spent a lot of time alone. A LOT of time, and much of it was most of a lonely aloneness. But in that time, I had a lot of time to reflect on a lot of things...and there were times where I'd be out walking on a path along the canal, alone, and I'd get this intense feeling from the very depths of my chest, bubbling out and up and around like joy and sorrow and desire, and it would be overwhelming. It's something like understanding, but I'm not sure that I really registered anything to understand. I just was, as pure and simple and corrupt and complex as I was meant to be, and that's all that mattered.
That still happens, but not nearly as frequently, mostly because I'm not alone or exposed to nature as much.
I don't get as many instant connections with people, but I do on occasion. When I first met my ENFJ friend, it was only for a little while at a convo at the start of my school. I didn't talk to him for at least a month or two after that. Now, I don't remember people. I suck at that. I don't remember who I met when or where or any of that. But I distinctly remember how I met him, even though I can't recall the events for anyone else I met in those days. There was a kind of connection there, I think.