Timer of 12 seconds using hardware circuit
You could use a Schmitt-Trigger with an RC-LP on it's input and two different resistors for charging and discharging. If Input A goes low, C1 will be discharged via R1. Use a time constant to create 12s delay till the Schmitt-Trigger goes low.
R2 determines the time it takes the output to go high again, after A went high.



Alternatively, you could obviously use a small µC like an ATtiny. This would give you a lot more flexibility.