If I were charged with preventing a bowhunter from getting target panic and could make only one change in their form or equipment, I would take away their trigger release and replace it with a hinge-style release aid.
Back-tension, hinge, pull-through, or trigger-less release aids (these names can be used interchangeably) will not prevent or cure target panic on their own. However, they will help to restructure the shot process and retrain the subconscious and conscious mind. These release aids expedite the "healing" process, and also work as a preventative tool for those who have never had target panic but want to avoid it.
The primary reason to shoot a hinge-style release aid is to make the shot a complete surprise. They don't have a trigger, and are designed to make it nearly impossible to precisely time the shot because you rotate the handle around a pivot point until it fires. This reduces the anxiety associated with the "timing" of the shot, because you can't anticipate when the shot will go off. You are forced to maintain focus and stick with the shot. Eventually, using a hinge release will allow you to hold steadier on the target and your anxiety will wane.
The first question that comes up regarding back-tension releases is, "What is the best way to shoot this thing?" The answer is simple: Use the method that works best for you! There are many ways to execute the shot, so try different methods until one gives you the most consistency and, most importantly, the least anxiety surrounding the execution of the shot.
Most hinge releases can be set up so that they "click" right before they fire. In my opinion, this click defeats the purpose of using the hinge release. Shooting with the click transforms the back-tension release from an absolute surprise release aid into a trigger release. Once you've reached the click, the handle becomes a trigger that you can punch! If you are using a hinge release to break bad habits, please don't use the click! Eliminate it by rotating the release's half-moon 180 degrees (see manufacturer's instructions).
Start the learning process by using a length of string as a "pretend" bow. Pull the bow back by placing your thumb over your index finger to prevent the handle from rotating and firing the release. Maintain tension on your index finger as you pull the bow back. Your other fingers can be engaged on the handle, but do most of the pulling with the index finger and thumb.
Once the bow is at full draw, find a comfortable anchor and begin aiming. Remove your thumb from over your index finger. Begin to relax your index finger, while at the same time contracting the muscles in the middle of your back, between your shoulder blades. At the same time, engage the ring and pinky finger more snugly on the handle of the release. These motions in combination act to rotate the release handle gradually and nearly imperceptibly until it fires. Keep your release hand as relaxed as possible.
Most bowhunters don't like the idea of using a hinge-style release aid for hunting because they want to be able to precisely time their shot. A hinge-style release precludes them from doing that. I understand this sentiment completely. I only hunt with a hinge release when I'll have plenty of time for the shot, such as when spot-and-stalk hunting for mule deer. For elk or whitetail hunting, I always use a trigger release, because the shot often needs to be executed quickly.
If you're serious about your long-term archery shooting skills, I would encourage you to do most of your practicing and shooting with a hinge release. You can always switch to your trigger release aid for hunting. If you're shooting both releases correctly, the impact points should be very close. If necessary, you can re-sight in for the trigger release aid with a very minor gang adjustment of your pins. I go through this procedure at the beginning of every hunting season.