1964 chevy 327 V8 - has new alternator, starter, relay & regulator and has all new wiring.

Why does the generator light stay on when the car is idling and the horn won't work?

Did you wire this yourself? What is the voltage output at idle? Which do you actually have a generator or an alternator?

Remove and fully charge, or replace, the battery. Also, the idle rpm may be too low.

Verify the system is wired properly but I would also have that new alternator tested. NEW stands for Never Ever Worked and I have had NEW parts handed to me that were faulty. Just sayin'...