A couple points about your parts list and plans:
1) You're linking to a Zener Diode, which is probably not want you want. You probably want a regular old diode. Zener diodes are designed to allow reverse current flow when the voltage potential exceeds a certain preset, in the case of the one you linked, 12V
.
2) That 3-pin flasher module you've linked sounds like its intended to flash at the same rate as typical turn-signal flashes, which is significantly slower than what an F1 rear blinker would flash like.