Is it safe to use a lower rated cable to power a higher amperage device if it isn't constant?
There are two reasons you want a bigger wire for more current:


Voltage drop due to resistance — i.e. your signal is attenuated too much. You can figure out for yourself whether this is acceptable experimentally, or by calculating or measuring the resistance of your wires and modeling the effect on your circuit.
Overheating (melting insulation and possibly then wire) due to resistive heating. For this, only the average current usually matters. More precisely — you're going to put in a pulse of heat energy
exactly as much as the resistive loss you computed for the previous
point. Then, there are two questions:


Does this heat immediately raise the temperature enough to melt anything? (Depends on heat capacity of the wire and insulation.)
Will the heat have dissipated sufficiently over the time to the next pulse so that the average temperature doesn't continue to rise until something melts? (Depends on how well the wire is cooled by ambient air etc.)



At the speed of an engine's firing cycle, you almost certainly only have to worry about the average current (heat moves slowly), and the reduced wire gauge will not be a significant issue for heating of the wire. The voltage drop may yet be a problem; you'll have to work that out yourself.