I never take their eggs when they're watching. Turkeys are very emotional, and I don't want them to think that the nest is insecure and go lay their eggs somewhere else. It can be hard to find the free range turkey nests. I have one hen who dug a hole behind a pile of branches, and covers her nest with leaves every time she finishes using the nest. I leave 1-2 ceramic eggs in each nest so that they keep using the nest, but not so many that they think that there's enough to brood.
You can let them brood their own clutch any time you want, and they go broody. Different individual hens will finish laying at different times, so if you wait too long they may stop laying without going broody on your schedule. Certainly you'll maximize your hatch by collecting and incubating every egg until the very end of the season, then let them brood the last eggs, but sometimes your schedule and their broody schedule don't agree. so you may miss the opportunity for them to brood if you wait until the last minute. When they will stop laying depends on the individual birds, and where you live, which determines how long your photoperiod is. If they're over 2 years old and you just got them, you might contact the previous owner to ask when they started and stopped laying each year, and how often they went broody.
When you decide you want them to go broody, you can either stop collecting the eggs, or you can continue collecting and storing, but add 1-2 ceramic or throw-away eggs to the nests every day. That may encourage the hens to start brooding, since they tend to brood only after there's enough eggs in the nest. Once they've held their brood for a few days, you can put all the collected eggs under them at the same time, so they will all hatch within a short time, and you don't lose poults because of a staggered hatch.
Thank you for this info! I have a girl thinking about brooding (I believe).