Sorry for my absence (I had to sleep). I think we might be talking about two different aspects of the same thing ... but,

if we use as reference the point on the surface of the earth farthest away from the sun at the moment the centre of the earth is farthest away from the sun (i.e. solstice), then

the hours of darkness (night) at that place either side of that moment should be equal, no matter what your longitude, no?

BTW, I appreciate the patience in my enlightenment.