Circuit IC part number and / or circuit sketch needed so as can count to 2 , up counter with automatic reset with input initiated by Hall Magnetic sensor. 12121212. The 2nd pulse will initiate NE555 monostable timer with an output pulse to turn on transistor that connects a different terminal to ground for milliseconds of time.

 

Microchip 10F222 and a bit of code should do the trick, and you could dispense with the 555 as well.

 

How long will that pulse need to be?? A CD4017 can count up and the higher outputs can easily frrd an OR gate for up to 7 or 8 count intervals until the reset arrives.
AND, for once the TS has stated the requirement at the very start of the thread, without asking how to make something work. I applaud that correct process!!