You can install any lamp that fits the socket. Unless that socket is crimped into the reflector (like on these old GM cars) you could easily change the socket to accept any lamp base, but to do so requires a separate ground wire (and figuring out how to mount the socket so it doesn't fall out).
Sequential flashing lights are not about the lamp or the socket but the flasher and the circuitry. You can not sequentially flash a rear lamp where they are all powered by one wire, it has to have three separate power leads if you want to flash three lamps. The flasher itself can be an electric 12 volt motor spinning a rotating disc that has contacts on the disc for the lights to illuminate (analog) or a computer circuit that amplifies a decay counter to fire the lights sequentially (digital). Either way to need to add four wires to the cars wiring to light the rear lamps sequentially. This assumes three lamps per side but you can add more lights for a greater affect.
In 1965, the analog motorized turn signal flasher was first fitted on Thunderbirds, soon after followed by Mercury Cougars (1968-1970), and the Shelby Mustang (1968-1970), and the 1969 only Chrysler Imperial. Rock Auto may have these flashers still on the shelf as a replacement part. Modern Shelby Cobras have the digital flasher which is wired into their harness as opposed to a separate part. Suppose it can be picked out but it will be expensive.