Even after four years of having ducks i am not sure weather ducks can see in darkness or if they are as blind as a mole!
My ducks have a duck-house with plenty of packages as nesting boxes, straw, hay, dry leaves, basically a duck's paradise and they have their duck-run, exposed to the elements where they have access to water and food 24x7.
For security reasons i have d2d lights around the house and a work-platform side by side to the duck-house and run, so when they are out in the run, they are in a relatively well lightened environment - think like street-lights.
There were always ducks sleeping in the house and ducks sleeping outside in the run.
Then last fall i covered the wall between the duck-house and my work-platform with a dark tarp for more weather protection and as a result all ducks refused to go into the house that evening. They all slept in the run. Assuming that it was too dark inside the house i installed a night-light inside and next evening order was restored. ¾ of the ducks went inside ¼ slept outside.
The inside of the house is divided into a mud-room (at the entrance), a living-room and two bedrooms, accessible from the living-room. The night-light is installed in the living-room, and brightens up the mud-room as well as one of the bed-rooms. What i have observed - i also have a camera in the duck-house - is that it the ducks are trying to sleep in their preferred darkness-zone. Some always sleep in the very dark bed-room while others prefer to sleep in the brighter living-room.
As for the impact on egg-laying: Early spring is the time when my ducks lay most eggs, they lay far less eggs during the high-summer, when the days are the longest. I doubt that a tiny night-light has any measurable effect on a birds egg-laying cycle. - I also have seen what kind of lights are being used to induce egg laying in egg-factories, those lights are as bright as the sun on a clear day and the hens do not sleep when the artificial light are on.