Double check your courtesy, rear compartment or Coupe dome light socket before you decide to replace the bulb and socket, it could be the source of the problem. 1963-1967 Convertible Interior Rear Compartment or Under Dash Courtesy Light Socket.
Includes new light socket and terminals.
Convertible: Rear Compartment Light
Coupe & Convertible: Under Dash Courtesy Light
Coupe Dome Light