The workaround is to trick Thunderbird to not pay attention to that new notification.
Two steps:
0) First, make sure you're subscribed to "All Mail" if you (like me) thought unsubscribing would solve your problem
1) Create a filter to mark new items in "Sent Mail" as read. Tools -> Message Filters -> select the gmail account -> New
- apply when: checking mail or manually run
- match all of the following: [from] contains [youremail@gmail.com] perform these
- action: [mark as read]
- OK
This way Thunderbird won't think they're unread. However, at least on my machine the account name still highlights blue and a notification sound is played (perhaps because it can't run the filter fast enough?) So, step 2...
2) Right-click on "All Mail" -> Properties -> General Information
- UNCHECK "When getting new messages for this account, always check this folder"
- (you probably also want to uncheck the other box, "Include in search results" so you don't have duplicates in search results, but that's a different issue)
- OK
Send a test message to yourself or some bogus account to test it, but it should no longer give you a sound notification or turn the account name blue.
EDIT: I discovered that after doing this, new received items still show up twice (once in inbox, once in All Mail), which is suboptimal. I found that simply unsubscribing from All Mail after performing the above two steps solved this last problem without affecting the sent mail problem.
You should make this portion into a question and then put the information you found in an answer. – jonsca – 2012-11-09T04:09:52.447