As a teenager, I had a number of times when I'd be hiking through the woods to a stand in the dark, and I'd hear something walking parallel to me in the woods. Whenever I would stop, the sound would stop. As soon as I would start walking, I would hear it again. I spent a lot of time stopping and shining my light around... The best scares would come when that was happening, and I was kind of nervous- and then a grouse would flush close by. After that I'd stand there swallowing hard to keep my heart from pumping itself out of my chest. I kind of miss those days.
I lived on a farm in Greenbrier county WV years ago...it was a 1 1/2 mile walk in or out as I had no 4wd at the time. I worked as a "river rat" on the New and Gauley rivers. Anyway I had the exact same thing happen to me....made the hair stand up on the back of my neck type thing. Turned out to be a Bobcat.
Odd as it sounds that Bobcat became my friend and company as it followed me in and out most all of the time. I thought it was really cool, but it scared the crap out of me at first cause when I moved, it moved.....I stopped, it stopped.