I have used a work around for the slow tavern generals, if you go to the adventure and click the generals tab and wait until you see the generals are on the way they arrive at the proper time. I hope this helps
legend has it that it's caused by someone trying to whisper you when you're offline, though not sure how that rumour started
After all these years a workaround solution should have been applied if the original problem can't be tracked. When the "begin tab flashing" function is called it should check how many open chats there actually are; if none then cancel. At minimum its possible stop the flashing when the 1:1 tab is selected once.
The key to bug fixes is being able to reproduce them - there's no doubt. I wish I could help. I would estimate it happens 1 in 100 times I log in (therefore maybe once per month) and that makes it hard to collect any data. If I come up with something I'll make sure to post it.
Sorry, but I've slept since then...
I believe the flashing whisper tab is caused by the way how the chat client gui and connection to the server and chat channel gets initialized. When the tabs are drawn and the chat channel for that tab is initialized sometimes the connection is created before the gui is ready and the channel "motd/welcome" is printed causing the tab to flash (just like help, trade, guild, guild officers tabs flashes/lights when those channels are initialized). If this happens on whisper tab before the tab gui is ready it starts to flash and when the gui gets ready it clears the "motd/welcome" text but not the flashing tab. If you are quick enough you can see the "motd/welcome" text on the whisper tab before it's cleared by the whisper gui.
I don't know if the whisper has it's own chat channel but I've seen a "motd/welcome" text printed on it when the chat client tabs are populated.