Here's some more thought- but no idea where it's leading...
The vents are probably not activated until a fan setting is selected. Maybe that's why you have to have the fan on.
In the del Sol, for example, the AC isn't actually on until you turn on the fan. Maybe GM links all the climate controls with the fan.
Also, it's interesting that the sound isn't made at idle- when manifold vacuum is highest. Could be a clue.
Perhaps the same style of climate control parts are used in other GM vehicles- a search of GM enthusiast sites on the internet could be helpful to you... say camaros or corvettes? Heck, even the trucks have club sites these days...