Ideas for a 12V brake light flasher circuit

You could do it with two 555 timers, one for the flashing and a second with a one-shot. Combining them to get the results you need might take a few transistors.

If this is for learning or a fun electronics project, start with the datasheet for the bulb. With the datasheet information you'll learn what your circuit needs to provide to the bulb for proper operation. Then you design the circuit to provide that. And yes, it can be done at 12 volts.

If you intend to actually install this on the motorcycle, you'll need to consider the environment - heat and cold, sleet, rain, snow, dust, mud, vibration, etc. There will possibly be legal/insurance/safety regulations that apply.

Ed

A simple way would to use an Arduino micro processor. It would require learning how to program it. It would be a very simple program, just tell it which pin is the input, count to the number of off and on times and how many times before stopping. Then a transistor or other power device on the output to handle the current of the bulb. Those Arduino boards from China are less than $ 5.

It should be possible to remain in the 12V domain, possibly using a 4060 which is a counter and a timer in one part . HEF4060 CD4060 MC14060 etc.

Perhaps a diode from pin 4 to pin 11 to stop the timer, output from pin 7 to a P-channel MOSFET to control the lamp, timing circuit on pins 9,10,11 and a reset circuit on pin 12.