How do I back-up 'Thunderbird' e-mails?

I have an iMac and use Time Machine for backing-up. When I bought the iMac I used Mail as my e-mail tool, but I had all sorts of problems with it so switched to Thunderbird (which I find much better). I store to-be-retained e-mails 'within' Thunderbird using its 'Local Folders' facility, where I have a structured set of folders, sub-folders, sub-sub-folders etc.

From what I can work out, Time Machine does not back-up anything in 'Local Folders', never mind Thunderbord's standard folders such as Inbox, Drafts, Sent etc. Is this True?

Assuming it is, I've contacted the Thunderbird support community for guidance as to how to back-up, and I've had a response from a non-Mac user. He's pointed me to some documentation, the key point being that I'm to back-up my Thunderbird 'profile' which can be supposedfully found in Macintosh HD/Users/john (my username)/Library. There's a problem here in that I can get to Macintosh HD/Users/john, but within 'john' there's no 'Library'.

Help please.

Regards

John Bugler