We dealt with it in Western NE were I grew up as well. I have pictures of paw prints in our garden after it had been tilled, and tracks in fresh snow that followed my dad after he walked around the house early one morning...that was pretty wild.
9/10 you will never see them, you might hear them "scream," but rarely will you actually see one...I would bet you are right, however, and those eyes were attached to a murder cat.
Our coyotes here in KS are getting pretty brave, as long as they are out of the light they will watch for a bit. I've had them right up to our front door on our acreage. We can get a special tag to hunt with artificial light or night optics in the winter months...I'll be purchasing one this year.