Mail.app + Gmail IMAP: my deleted msgs are not deleted

Following are my test results in both Mail and Gmail/web

- deleted msgs in inbox are grey but not removed
- gmail prefs, checked Trash for 'show in IMAP'
- now trash shows up under Gmail but is empty
- mail prefs, set "Use this mailbox for Trash"
- now I have two Trash folders under Gmail, but under Trash I do not
see this gmail account listed (the account is correctly listed under
Inbox, Drafts, Sent
- In one of the Trash folders under Gmail, I deleted all the msgs.
There was Activity, but msgs are still there.
- In Gmail/web I invoked "Empty trash now" for all 122 msgs.
- In Mail, I invoked Synchronize <this gmail account> -> deleted msgs still there
- Run Mail Vacuum automator script
- When Mail relaunches it does IMAP synch
- now have only one Trash folder under Gmail, but deletes are still
showing in Inbox grey
- Undelete one msg - seemed to work - try delete again - synched with
IMAP but msg is still there.

- Gmail settings: I think the problem may be related to following exactly the Gmail help "(access Gmail froth other clients using IMAP)

- Mail.app prefs, I have set according the Gmail help as follows (only store junk on server is checked):

<<<
Apple Mail

From the Mail menu, click Preferences > Accounts > Mailbox Behaviors

Drafts:
Store draft messages on the server > do NOT check

Sent:
Store sent messages on the server > do NOT check

Junk:
Store junk messages on the server > checked
Delete junk messages when > Never

Trash:
Move deleted messages to the Trash mailbox > do NOT check
Store deleted messages on the server > do NOT check

Any suggestions would be mucho appreciated!

Message was edited by: Steve Darden