I agree--grey squirrel.
I live in NYS. I can personally attest to the fact that squirrels will conduct nocturnal Olympic contests. It took me a really long time to evict the squirrels living in the roof of a brick house I lived in for a while. And they would start up at all hours of the night, running/jumping/scrabbling around--
inside the roof, above the plaster ceilings. So I assume that, if they'll do that once they're inside, they'll do it trying to get in, regardless of the fact that, generally, they may not be considered nocturnal.
I trapped them, one at a time, with peanut butter in a Have-a-Hart trap, off the front porch, directly in front of, and below the holes they were using over the front porch. First, I sealed off the two holes they were using, over the eaves troughs, with sheet-steel, riveted in place.
They had one remaining hole, directly over the porch. So...I made a one-way "squirrel vavle," by covering the hole with 1/4" screen, then cutting a squirrel-sized hole in the screen (use a "cross" pattern and leave the four "leaves" of the cut attached--don't cut a circle.) Then, I bent the four "leaves" of the screen outward, around I a small hole they could crawl out of, on the theory of a minnow trap, i.e., allowing one-way passage only. I don't know if this ever worked but finally, out of desparation, I took the screen off and, one afternoon, I went out for coffee. Unbelievably, on my way out,
I saw (what turned out to be) the last last squirrel, just inside the hole, looking out at me, through the (now unscreened hole). He looked me right in the eye, through the hole over the porch, after I had removed my "squirrel valve," which he may have been afraid to pass, for a couple days.
Perhaps he was thirsty, or felt confined, by my "squirrel vavle"--I dunno. But when I came back, I had the feeling he was gone, and closed up the hole with 3/4" plywood, then stapled 1/4" screen all over the wood sealing the hole up, and that was that. He really was gone, and I suspect that it was because he hadn't felt like going through my squirrel valve, so that he felt confined in the roof for a few days.
So...you might consider blocking them in for a day or two, so you can control a "pulsed egress" and let them out. Apparently the trick is to go out for coffee, come right back, and seal off their access, after they've gone out for the afternoon.
On the other hand, they can get mega destructive if they feel trapped, so don't go far from home, if you try this method. My buddy had one shred the woodwork in his basement, near the windows, trying to get out--I don't think anybody ever figured out how he got in.
And they can make a
lot of noise in a quiet house--I was convinced I had "roof rats" until I saw them hanging around the eaves too consistently, and finally figured it out. You can hear them scratching, even, (and I mean, scratching their own fleas, or whatever--when they start in on the wood, that's even
louder) in the middle of the night, and thumping and bouncing around.
But they do have a weakness for peanut butter, as has been noted. Peanut butter is perhaps your greatest weapon...I used Peter Pan "Chunky"--YMMV.
Good luck.