I recently camped at Harriman State Park in Southern New York, in early October. Upon returning home, I noticed that I had a passenger with me.
The caterpillar in question is an almost translucent, pale green color with a single reddish stripe running down the center of the back. It is approximately 1.5 inches long, with a reddish face as well.
I tried using a caterpillar identification book, but the closest one I could find also had a split tail, which this one does not.