= Solution
If temporal variation is spatially uniform, summing all frames in each group still gives independent <Poisson distribution> totals, but their means may now be $N_A,N_B$ with ratio $c=N_A/N_B\ne1$. At high counts and negligible <read noise>, direct propagation gives
$$
\operatorname{Var}(A/B)\simeq\frac{c^2}{g}\left(\frac1{N_A}+\frac1{N_B}\right).
$$
After dividing the ratio image by its measured mean $c$, the appropriate estimator is
$$
\boxed{g\simeq\frac{1/N_A+1/N_B}{\operatorname{Var}((A/B)/c)}.}
$$
The original formula is recovered only for $N_A=N_B=N$. Uniform brightness drift does not automatically create a spatial pattern or extra ratio scatter beyond these changed noise levels; its leading problem is unequal group normalization. Interleave the groups in <time> or pair exposures of comparable flux, measure their separate means, and propagate shot and <read noise> when rescaling. If the spatial pattern or <photodetector> sensitivity also evolves, the ratio develops systematic structure that must be modeled or those frames rejected. A normalization inferred from finitely many <detector pixels> introduces a small shared correlation, which vanishes in the large-pixel limit and can be included in a precise uncertainty analysis.
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