Time Machine restore of Mail (and sync with Gmail)

I asked my wife if she could look at some unread emails and sort out some emails in a particular folder.
We use three gmail accounts and sync all three to several desktops (including a Mac 10.9.2) and other devices.
Upon my return home she was giggling about the fact that she'd accidentally moved everything to the trash. All that remain are the emails in the bin which are younger than 30 days.
Fortunately we use Time Machine on the Mac. I am trying to restore Mac Mail to a time shortly before her actions in the hope they will upload back onto Gmail.
Have tried it once, restoring the folder called V2 under ~/Library/Mail and a large number of files were copied from the external hard drive, but they didn't seem to make it back into Mail and logging into the accounts direct to gmail confirms nothing has been restored. Can anyone give me some pointers; I must be able to do this somehow?
Thanks, Richard

Mac Mail is somewhat more difficult to do a restore. Other than restoring your entire hard drive, here is the method I used:

Open your Mail program and leave it open. Make sure your Time Machine external hard drive is attached and enter Time Machine. Select a date from the backups (pink color) that you know the mail can be restored from. Time Machine should then open mail from the backup. Select restore. It shouldn't ask for a path if I remember correctly but if it does, just direct it to the original Mail. Let us know if this works for you as it has been quite a while since I performed a Time Machine restore of Mail.

Thanks chscag,
I tried this a moment ago. The blue bar at the bottom left of the screen showed thousands of incoming mails (a good indication) but 30 minutes later we are no further forward, except to say that a on the navigation bar on the left of the Mail window, "Time Machine" has appeared under the heading "ON MY MAC" but with no content.
I considered this method yesterday, but I thought it would only restore the mail application, not the content. Just to clarify, I use IMAP for the three accounts.
Many thanks for you time in suggesting this

I've now resolved this. To begin with I was a bit panicked, but after having had a cup of tea and taking a fresh. calmer look at the situation, Mac Mail provides instructions on screen how to restore, either by mailbox or by highlighting particular messages. I recovere them from the [Gmail] folder. It restores them into a 'Recovered Messages' folder in Mail from where they can be dragged to the appropriate folder.