And what would happen if all birds become extinct?
This is why I think Bob's rule isn't the exact rule that is taking place behind the scenes. The 'first' bird is just attuned to the rule. In the absence of any birds, there may be something else that has an effect by being attuned to it. I mean think of some of the rules of physics. We have generic equations that work in most conditions but when stretched to extreme conditions these generic equations are proved false and we now need better equations to model what works. The 'first bird crow/birdsong' is a generic rule which then gets replaced by some other model.
A better option would probably be dawn or dusk or something.
This is a better option, some wave that sweeps over the Earth, but this would require a sweeping mortality/immortality wave on Halloween. If immortals want to continue on with their feeding, they'd need to keep up with this wave until the entire conjunction ceases for all portions of Earth.
It seems the end of the day is something that lags dawn but during the night/early morning. (you can get further discrepancies at the polar regions where you get near all light 'days' or the opposite.