I just start making a pile of golf balls or fake eggs, I start with two, then add one each day.
I've tried that four or five times, even used marked real eggs once instead of golf balls. I did get a broody hen once, but that was in a different nest so I don't think that counts. I had hens that would sometimes go broody.
One time when I went to visit the grandkids the chicken sitter failed to collect eggs at all. The eggs piled up pretty thick in those few days. When I got back, after dark, two hens were siting on two nests, sort of acting broody. When I removed the eggs they were no longer acting broody. If I had left a bunch of eggs in there one or both may have actually gone broody but I didn't so I'll never know.
Many hens have had going broody bred out of them. A broody hen is not productive, she is not laying eggs. And they can be disruptive to an egg laying operation, requires special handling. If the person deciding which birds get to breed only hatches eggs from hens that don't go broody, after a few generations you have a flock where most hens don't ever go broody. They use incubators to hatch the eggs.
Some hens of any breed can go broody, some hens of other breeds may never go broody. It is very much up to the individual hen. Many of us have hens that hardly ever go broody, the hatcheries have bred that out of them.
I agree that I am more likely to get a broody hen in the heat of summer, even without letting the eggs build up. When I tried letting the eggs or fake eggs build up it was May, trying to get a jump start on it. It did not work for me.
@CSDeVault I suspect that you have hens that have pretty much had the broodiness bred out of them. I had a couple of Buff Orpington that never went broody and they are a breed that is supposed to go broody a lot. You can try letting real or fake eggs build up, but the only way you can control hatching eggs is to get an incubator.