Which kind of precludes the archer not knowing the invisible creature is there.
Not in the slightest. We aren't talking about getting into a wrestling match over the bow, or the like. All that's really needed is the equivalent of something that makes the archer flinch, or glance away for a moment in distraction. It doesn't have say, "YOOHOO I AM HERE!!"
"Gee, the bowstring felt weird just now," does not advertise someone present.