headlights blinking

Sounds like a faulty overheated headlamp switch. Also replace the wiring connector as it is probably quite damaged/ melted, etc

Convertible top switch on center console flashing emergency red brake sign on cluster will also blink your lights, with emergency brake off move the conv.top switch up and down and see if the emergency brake light flashes on your console, if not a convertible faulty emergency brake handle (contacts).