I see we are having trouble with the definitions of words. This word, "muting" is what we call "grounding" or, "shorting". This becomes much easier now that we have solved the language problem.
The real goal is to use the oil switch to kill the engine. Pressure switch is closed to ground while starting. After engine is running long enough to get oil pressure, if switch closes, activate something to short the primary of the coil to ground, and keep it grounded for at least 5 seconds, even while the power from the magneto is failing. True?
I think even simpler than a 555 timer chip.