You can have each tower derive a perfectly stable 1Hz signal from the mains, but you have no way to synchronize those signals. Each tower's 'tick' starts at a random point in the 60Hz cycle.

You need an external, dedicated channel for this. You either synchronize with signals sent between towers or with a global signal from somewhere else (space). GPS broadcasts atomic time references for free, so everyone just uses that

Definitely GPS. Other methods have been used in the past--I remember reading operating reports from a wind farm nearly 20 years ago that slowly brought all its lights in line with each other over several months--but these days you can buy mainstream lighting with the GNSS receiver built in from a number of suppliers. They make it easy.

For wind farm use most also have an external input for ADLS triggers, though that usually also requires a separate controller and communications connection to manage the ADLS signals.

The flashing red lights are L-864 type. The requirements are 20 to 40 flashes per minute (FPM), and typically 30 FPM is used.