I cheek the stock, then look over the barrel(s), shooting instinctively, I guess. I might see the barrels in peripheral vision, but not consciously. Both eyes open.
I pass the 'bird' and slap the trigger when "just" 'touching/passing'.
With my flinter 20 bore, I have to pass the bird by close to a foot, before slapping the trigger in order to hit, due to the slower ignition sequence.
I find modern shotguns identical to cap-locks, for shooting flying birds, clay or feathered. This method works at all ranges, btw. It automatically gives the correct lead.