Here is something you can try. It works here for my linux system which had
the same problem.
First install the Gmail extension.
Re-start TB
Now while TB is running goto your TB profile directory, Find the Gmail
extension folder ( usually {860a7040-44a3-11da-8cd6-0800200c9a66} is the
name here). Now make this folder read-only. This must be there for the
Gmail extension to work. When you update to a newer version this folder
will need unlock and re-lock after update is applied.
Now restart TB and your gmail should work. The extension will not appear in
the add-on list but is still there. For some reason TB is having some kind
of problem keeping it installed. It is deleting the folder on re-starts.
Hope this helps you out.
KE4AVB