Clean 12v switched source that is hot cranking and running

I'm not much of a designer, but there's no reason you could not buy or build a little delay circuit that runs off IGN1 / IGN2 and will hold that "on" for say, 1/4 or 1/2 second before dropping off line. That would take care of any delay or spike between the switchover from IGN2 back to IGN1 and yet would not be so long as to cause a problem at shutdown.

A "redneck" way to do this is with a large capacitor and diode

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But for this to be effective you need a more delicate relay with a high resistance coil that draws less current.

How this works is, the tag end of the diode would be connected to IGN1/ IGN2. When that goes dead, the diode prevents the cap from discharging into the the rest of the harness. The cap discharges into the relay coil, holding it engaged fro a short time. This would be a "try it" setup you would need a parts "junk box" to get things to work