Last month I started my '63 after 2 years of sitting. None of the electrics worked except the headlights. Not the antenna, the rear lights, nothing. But as the car idled, eventually everything began to operate normally. The only issue left was the the rear turn signal light on one side. Oddly enough the brake light worked but the turn signal didn't. And I had the same rapid flasher as you. Changing out the bulb did nothing but cleaning up around the outside of the socket and insuring it got good ground did. The sockets in these cars are the ground.