Are you using the halo of the light only to shine the critter and you arent able to identify what it is or are you shining he critter with the full power of the light? One thing you can try doing if you don't have that powerful of a light is actually putting the light and shooter down wid further from the caller if you have a remote capable one. Predators and especially coyotes will almost always circle down wind at night. And in my experience, the later in the year usually means the further down wind they will circle.

It is better to be hated for who you are than to be loved for who you are not...