Check out the IPSC sites - those small, short re-dot sights are amazing. I was looking at a couple 'race' guns with them mounted atop the slide, the other day - impressive - & exceptionally fast to pick up on target with a handgun - would be even easier with a rifle, adjustable for intensity and able to see the dot, even against snow when set high enough. Some start as soon as the cover is removed while others have switches.

I would be looking that direction, unless I had to have objects magnified as with a scope.

When mounted, it would probably be lower than the hammer's ears.