This^^^When mine got to laying age, I kept them in the run until late in the afternoon when I was reasonably sure they were done laying for the day. The nest box was the most optimal spot so it was a natural choice for them to lay in there rather than in the run. Once they get into a habit, they usually keep doing it. So my goal was to make the habit using the next box. Conversely, if the habit is laying in the bushes or wherever...that's hard to break too. Usually requires confinement until they lay where you want them to lay.
Using fake eggs/golf balls in the nests as 'bait' can help entice them to use the nests.
'Privacy' is subjective...the nest must feel secure to bird....some lay in open topped bins, some nests are boxed in.
I fashioned my nests to be like the old metal round holed nests, they seem to like them.
Oh and I collect at different times depending on weather, if it's wet I gather more often to avoid muck being tread into nests and onto eggs. When it's freezing I gather more often to avoid frozen eggs. When it's fair, I gather when I lock up coop at night.
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