Turning on and off car ignition - created two pulses?
I'm assuming you don't want to use a microcontroller for this, so here's a 555/logic based idea:



Disclaimer: I threw this together in 5 mins, and haven't used a 555 timer for ages, so I may have made a mistake (or three)
Anyway, the basic idea is simple, set the 555 up in monostable "one-shot" mode, and use an inverter gate and a couple of caps/diodes to produce negative pulses on ignition on/off. The inverter gate can be anything that has a reasonably low output impedance.
The inverter power pins are not shown, and ignore R3 (it's just there for SPICE simulation purposes)   

Here's simulation of the circuit (on/off time of ignition shortened from "normal" use)
The ignition starts the simulation on, turns off at 1 second, and turns on again at 11 seconds, each time producing a 3 second pulse at the 555 output (this can be used to drive a transistor to switch your GoPro):