After starting my 2001 Volkswagen Cabrio and all the bells and whistles stop, I can still faintly hear a buzzer-like alarm. What the heck is that?

let me get my crystal ball- hmmmmmmmm- I see a seat belt not fastened-

Nope, Carnac the Magnificant, the seat belt was fastened securely (I checked). This is a very, very faint sound. If I had had the radio on, I wouldn't have heard it.

Most all warnings are never faint. See if you are getting any feed back noise through your speakers. If no speaker noise, the only thing I can think of is perhaps when you shut your door, the door ajar button is not down completely, which may be letting out just enough volts to make your door alarm buzz ever so slightly. If it persists, you can always start pulling fuses until the noise goes away. Then you will at least know what that fuse powers and where to start looking.

Thank you, I'll try pulling fuses. I'll let you know how it turns out!