Birdrain, you are right, I think, but it might make more sense if we took it apart a little bit farther. I suspect there are a number of factors that affect when peahens begin laying, whether they continue, and when they stop. In addition to light/daylight, there are also social cues and behaviors -- it seems to me that in any lekking bird, survival of the species depends on dispersed groups coming together at the same place (the lek) at the same time, in condition to reproduce (fertile).
When I think about the daylight piece of it, I almost visualize it as a math problem. We can look at the daylight factor in several ways: (1) by hours of daylight per day; (2) by changing hours of daylight each day (i.e., days getting longer or shorter); and (3) the RATE of change (i.e., are the days getting longer in larger or smaller daily increments?). When one lives near the equator, daylength doesn't change much, and the day to day change is minimal. When one lives up near Canada or Alaska, the day length varies a great deal from summertime, when the sun barely sets, to wintertime, when it barely rises. The number of minutes the day gets longer or shorter is higher than if one is living in South Texas or Florida. The rate of change is higher, the farther away from the equator.
Now if someone just happens to have light on in the coop 24/7, that's a situation the birds will get accustomed to, and as you say, may not affect breeding cycle. Yet when I have my heatlamps on 24/7, my hens start laying and my males start calling.... Here's the difference: in my case, I don't leave the heatlamps on all year. I only start running them once it begins to get very cold at night -- down to freezing or below. Before that, the days have been getting shorter and shorter. Then I turn on the lamps and leave them on 24/7, because that way the coop stays warm better -- the wood shavings absorb a lot of heat. From my peas' perspective, the days got shorter and shorter. Then the days suddenly get a lot longer -- and it happens overnight, so at a huge rate of change. As far as their bodies are concerned, they went instantly from "days are getting shorter" to "days last forever." The rate of change was enormous. The past two years it has triggered y hens into laying (not on purpose, of course), and it triggers my males into cherchez la femme mode....
It's a topic worth discussing... more later