I'm not familiar with microcontroller circuits. ...
This project could be a great way to get some microcontroller experience! The circuit is simple because you have just one input signal and one output signal. Here is an example schematic from a project
@KrisBlueNZ was working on when he passed:
The details are not important, but notice there is only one input, SW1, and one output, the drive signal to the gate of Q1, which was used to complete an external circuit connected to WP1 and WP2. The entire circuit was completed with surface mount components on a small disk-shaped circuit board that fit inside the base of a powerful flashlight. Several of us worked on this after Kris passed, so you would have plenty of help available to get your project up and running.
The biggest downside to using the PIC10F200 is programming it. This does require investing in an inexpensive "pod" that is temporarily connected to the circuit points labeled PP1, PP2, PP3, PP5, and PP6. The "pod" connects via USB to a personal computer, where you do the programming with free software downloaded from the Microchip website. You are done after your PIC program is downloaded from the PC to the PIC10F200 via the "pod"... provided the program works the first time, which hardly ever happens.
However, it takes only minutes to make program changes to correct errors and download the program again. After you have it all working (several of us here at EP can help you with that), the "pod" is removed for use again on another project. Presumably by then you will have become thoroughly addicted to using PICs and will reject the thought of ever again using a 555 for timing purposes.
... I was thinking along the line of a one shot using a 555, but getting two pulses when the input goes low has me stumped. Would prefer the output amplitude at +12Vdc (but could live with 5Vdc), and yes, this is an automotive application
That is so "old school" but perfectly acceptable for a simple project like this. As Chris mentioned, you need two 555 circuits as well as a pair of flip-flops, or a counter as he suggested, to count two output pulses and disable that 555 output when the pulses occur after the input goes low. When the input goes high again, that event would be used to reset the counter or the flip-flops in preparation for when the input goes low again.
The first 555 is wired to produce a single pulse on the low-to-high transition of the input. The second 555 is wired to produce a train of pulses on the high-to-low transition of the input, but after two pulses have been output the second 555 is disabled by the counter or flip-flops. You could "wire OR" the two 555 outputs to the base or gate of a switching transistor to create your 12 to 14 V output, so either 555 output going high (to generate a pulse) would cause your output to go high. You could also use a logic gate for the same purpose. Those are available now in single-gate packages for surface mount to use as "glue" logic. Are you proficient enough to work out the details, or do you need someone here to design a circuit for you?
The 555 and 556 timers are also available in surface mount if you want to go that route. Add some SMD Rs and Cs for timing purposes and a little solder and you are in business. Well, you do have to make some sort of circuit board, but
prototype boards with pre-made pads and traces are acceptable and readily available. Use what you need, cutting unused traces with a sharp hobby knife, and leave the rest. Feel free to add jumpers if necessary. I use 30 AWG insulated wire-wrap wire and secure it with a dab of hot-melt glue when everything is working to my satisfaction. Or use clear RTV cement and wait 24 hours for it to cure.