> hallmark Sidewinder grrrrr -> wheeeEeEeEEEEE growl comes from
That's probably this: https://en.wikipedia.org/wiki/Rolleron
That's probably this: https://en.wikipedia.org/wiki/Rolleron
We in the public don't have a complete list of missiles from various nations and their tones, but it's well known that American Sidewinder systems use an iconic growling dog[1] tone. Stinger is more sine like[2], and many others appear to be sine like too, and newer systems like 9X and later are clearly just digital and software based even by public descriptions of it.
What I'm suspecting is that, the early gen Sidewinder growl might have been just the raw sensor output piped into the headset, because the operating principle of those seeker units somewhat corresponds to the sounds, down to the high boresight angle warning tone which isn't hard to imagine a kid playing with a benchtop example and accidentally implementing it by damaging some cable.