Here is a movie of what 100 images in a stack, on a VERY CLEAR NIGHT, looks like if you look at frame-to-frame changes, and histogram equalize the images:
If you monitor 4 patches of 20x20 pixels each (one on the dark side of the Moon, one on the dark side sky, one on the bright side of the Moon and one on the bright side sky), you get these mean series:
There is some food for thought here. Consider the DS patch - it varies by tenths of counts (this is mean over a 20x20 patch) - the mean of that patch is typically several counts - so we are looking at several percent to ten percent changes with time here. Of course, we do not fit individual images, but only the stack average.
Notice how BS sky patch is dropping in intensity in this sequence - this is consistent with BS patch getting brighter - less light is being scattered to sky here.
If the sequence of images is scaled to the total flux of one of the images in the sequence we get a small drop in BS patch variability - it goes from 0.22% to 0.12%. SO either the shutter is variable and causing this, or the total amount of light in the 1x1 degree frame is variable, for other resons: scattering or extinction may remove light from the beam entering the telescope. But certainly, the light in the small 20x20 BS patch varies on its own even in flux-normalized images, so non-shutter variability is present.