In other words it stays low even in bright light or hot in the dark. It's the fact that the pixel's ADU value is not in proportion to it's illumination that makes it bad not the absolute ADU value. Using only dark frames gives you only one illumination level to test linearity with. I figure you can determine the general level of illumination by the average ADU value of the surrounding couple hundred pixels. Yes, I'd put it in the bad pixel mask.
Dark values are repeatable and can be subtracted out.
But I think these are just the easy to find bad pixels. Now you can take the histogram as below. OK, the experts will probably jump all over me. There are many more problems to come. But it is worth doing the experiment.