I also live in the sticks in the mountains of Kentucky and have something that is about my property. I haven’t seen anything but I have had my house beat on with wood in the middle of the night. I hear wood on wood knocks at various times and howls I can’t account for. Not coyotes, fox, raccoons or bear, I don’t know what they are. Strange chatter which sounds like a samauri movie on tv which we have heard several times. Working in the yard and hear a rock go whizzing by your head.
When the house was beat on the first time I was on the front porch that night about 10:45 and went around to the back and heard numerous, heavy footfalls in the backyard. I verbally challenged whom or whatever it was and threatened I had a gun and they were about to get shot and eventually fired off several rounds from an M1 carbine into the ground where I had a sliver of light. After the firing I heard something that sounded like a semi tearing through the woods headed deep into the Cumberland Mountain range in the middle of summer, not smart for snake and other critters about.
I have put up trail cams and security camera’s and have picked up nothing thus far. I just don’t know what it is.
Even deer and coyotes can see infrared beams - whatever is disturbing your property no doubt can see and avoid them, also. Putting up many cheap trail cams is good way to reduce activity around your house.