Timer sequence with delayed off and long trigger pulse
This circuit will generate a ~10usec negative-going trigger pulse on each side of an input pulse, which you can use to trigger your 555 monostable multivibrator: 







simulate this circuit &ndash; Schematic created using CircuitLab

It will operate directly from 12V, using 1/4 of a CD4077 ex-NOR gate. 

The input pulse should be reasonably clean and (more importantly) have reasonably fast rise and fall times. If that isn't true, square it up with a gate or two from the 4077 package or even a Schmitt trigger chip. 

It works by delaying one of the input signals by the R1 C1 time constant, so the inputs to the exclusive-NOR gate are briefly different from each other on both the rising and the falling input edges. 

Recalling the truth table for an ex-NOR gate, we can see that the result is that the output is high, with a brief negative-going pulse at each input edge: