To pattern a turkey gun, the sight is as important as the load and the choke.
Turkey hunters have four choices for sights. If you have an all-purpose shotgun, the factory beads work fine for close shots. You can upgrade to passive ramp sights. The next step up is an electronic optic. You can also use a telescopic sight, a scope.
Bead sights are the most imprecise of the suite because they don't really involve the target. They serve to align your eye parallel with the barrel plane to make sure you're pointing it at the right place. The problem is that beads are antithetical to the concept of shotgunning, which is the art of swinging on and leading moving targets. If your form is correct, you do not see the end of your barrel. You only see the target. Your brain computes in a split second all of the calculus necessary to place your shot column in a zone that will intercept the target.
Ideally, a turkey is a stationary target. If a bird is moving, your chance of killing it diminishes exponentially. A stationary gobbler stands erect with its head high and neck extended. The head and neck comprise the vital kill zone. If it is moving, it is a horizontal target with its head and neck retracted.
If you are aligning bead sights, your focus is momentarily on the beads, not the bird. It's a two-step process. First you align the beads, and then you shift focus from the beads to the bird. It isn't exactly inefficient. I have killed a lot of turkeys without using enhanced sights. It is merely the least efficient. Here's why.
Shooting at a turkey is not a snap shot. A hunter usually knows a turkey is coming and from which direction. The gun is shouldered, and you're staring down the barrel, sometimes for a very long time. It's a point shot, more like shooting a rifle.
An enhanced sight is much better for this application. This kind of sight is usually an add-on accessory that includes a red fiber optic at the muzzle and an adjustable green fiber optic near the receiver. Some employ a fiber optic ring on the receiver end. Your eyes engage and align the fiber optics immediately with the target always in focus. A ring sight aligns quicker than a fiber optic horseshoe.
For years, my turkey gun was a 12-gauge Winchester SX-3. Installing fiber optic sights improved my confidence immensely. I have not missed a gobbler with it, and all have been one-shot kills, largely because all were very close shots. I didn't miss any when it had only beads, either, but here's the difference. With beads I always believed I would flop a gobbler. With sights, I know I will.
You still must calibrate the sight with your choke and load. I recommend sighting in at 40 yards with a dedicated turkey patterning target that shows a turkey's head and neck area. I aim at the base of the neck. That accounts for muzzle rise from recoil, and it will concentrate the pattern on the head.
A 40-yard zero gives you full coverage to grabbing distance, but it will also ensure a clean kill to 50 yards. We don't recommend long shots, but sometimes a hung-up or reticent gobbler will force it on you.
The disadvantage to a fiber optic sight is that it relegates your shotgun to single-purpose. If you want to use it for waterfowl, rabbits or clay targets, you have to remove the sights, which means you'll have to recalibrate them in the spring. TSS and HeviShot are expensive. We don't like to do that.
An electronic sight is the next step up. It can be a red dot or a green dot. Some give you multiple reticle options. This is the most precise. Calibrated with your choke and load, you merely put the dot on the desired point of impact.
Three years ago, I switched to a dedicated turkey gun, a 20-gauge Winchester SX-3 with a cantilever rail mount. It has really good iron sights, but it is designed to take an optic. I mounted a Truglo electronic sight with multiple reticles and red/green options. I use green because I see it better than red. Paired with a Trulock turkey choke and No. 9 or No. 7 1/2 TSS, this combination is astonishingly effective.
The downside is that the sight is huge. It looks like a home entertainment system mounted on the gun. It does not inconvenience me, but there are a lot of lighter, more compact options available. If I were to upgrade, I would choose a Holosun sight. It is tiny, but it is also solar enhanced. This eliminates the potential of battery failure. Battery failures adhere to Murphy's Law. When it happens, it will always be at the worst time and always with catastrophic consequences.
Your final option is a telescopic sight, but it is not necessarily your ultimate option. A scope magnifies your target. That is a big advantage to anybody with compromised or deteriorated vision. Its disadvantage is that it can take some time to acquire the target. If a turkey pops into view at a really close distance, magnification can be an utter liability. It can also be challenging to remain engaged with a gobbler that's moving or bobbing and ducking its head while walking and pecking at things on the ground as turkeys often do.
A magnified target also presents a dynamic sight picture that can be challenging to keep centered. All of this translates to considerably more head and barrel movement, which increases the risk of alerting a gobbler.
Not many hunters use scopes, but if you need magnification, it is the best option.
Also, scopes and electronic optics can lose zero. It can happen by bumping or jolting the gun. Something that you turn on and off can reset itself inexplicably, or it can simply quit working. For that reason it is advisable to check zero before every season. Most of us don't do that. Again, Murphy's Law applies. It will cost you someday.
That will not happen with passive fiber optic sights, and it won't happen with beads as long as you call a gobbler close. Isn't that every turkey hunter's goal.