I use mouth calls rather than an electronic caller, and I find a quivering decoy is great in conjunction with my calling. The one I like best has a furry "sock" hanging off the end of a flexible rod. Sorry, I forget the brand name. It has a nice random action, and even between shakes the wind is usually sufficient to move the furry gizmo enough to attract attention. That's all it does IMHO: it attracts the attention of the coyote away from my position. Once a coyote makes an appearance, my calling is finished...the dog's attention is focussed on the decoy, and I do nothing to change that. In all honesty, a simple feather or piece of fluffy material tied to a branch is just as good as the commercial decoy in most cases.
I try to set up crosswind of the decoy. A lot of coyotes circle downwind and appear from that direction, so I don't like to be positioned directly downwind.
Love'em or hate'em, but it's hard not to respect coyotes. They provide some outstandingly fun and challenging hunting.