A few thoughts, as this is a good discussion for hunters, and I mean no disrespect to any posters:

LGP is a theoretical measure of the amount of light that will pass through an objective lens. The term "gathering" is a bit of a misnomer, as the lens doesn't gather anything. It simply allows light to pass through it, so a bigger lens naturally has more area for light to pass through. LGP is typically used in astronomy as sort of a "this telescope could be this good" way.

In sport optics for terrestrial viewing (binoculars, spotting scopes, and riflescopes), exit pupil is much more important than objective diameter, although they are linked. Exit pupil is a simple calculation of objective lens diameter (in mm) divided by magnification. You could also use a micrometer and measure the exit pupil and come up with the same result. For instance a 50mm scope at 10x has a 5mm exit pupil. The human eye when it is healthy and young will dilate to a maximum of about 7mm in low light. As you get older, this number gets a little smaller.

So, in low light your 7mm pupil is only making use of 5mm of exit pupil, because that is what your scope is showing it. If you go to either a bigger objective or lower magnification, the exit pupil will enlarge, providing a brighter image.

That is why when light is low, and you turn your magnification down, you see a brighter image: exit pupil.

During bright to normal viewing conditions, your eye's pupil will be constricted to a size that is smaller than the exit pupil of most scopes regardless of whether they are 40mm or 50mm (and aren't really high magnification), so the images will appear similarly bright. When light gets low, the bigger objective will provide a larger exit pupil, and apparently brighter image.

As far as shooting a marmot at 600 yards at 12x, I would feel quite confident at 12x. I would feel confident at 6x. Think of it this way: The marmot would be magnified twelve times, so it would appear 12 times closer. 600 divided by 12 is 50. Could you shoot a marmot at 50 yards with open sights?