If I leave it parked outside for a month and drive the spare car, will the
problem eventually solve itself?

First thing to do is DRY the car's insides. You might, for example, turn
the car heater all the way up and let is idle in the sun.

OR you can run an extension cord and operate an electric heater in the car
(taking proper precautions against the heater setting the car on fire.

Once it's dry you can "detail" the car and vacuum it as well .

If something literally died, completely drying it out should stop the smell.

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aem sends...