Of course, the seminal rules for keeping your own pet gremlin was to beware of exposure to water, sunlight, and the all important "feeding them after midnight." (This is a lot like children, although it seems (at least locally) to be more "exposure to sugar after school" that turns them into monsters...)
Is that "midnight local time," or...? I remember reading the novelization which suggested almost otherworldly origins, but I was thinking of adding gremlins into a Feng Shui campaign (they seem very Chinese-mythos to me...)