Far as I can tell, it happens every time I receive a whisper. Which means that every time someone sends me a stupid guild advertisement, or a bot sends spam at me, the icon in the taskbar will flash if I’m alt tabbed.
Can I turn this off just for whispers?
Not really. It’s embedded in the ChatFrame_MessageEventHandler function that handles all the chatframe events.
While the sound played when you get a whisper has a timer restriction around how often it is played which can be manipulated somewhat, the FlashClientIcon() function is straight out called for each WHISPER/BN_WHISPER. There doesn’t seem to be a corresponding StopFlash function to create a hook with.