Gmail won't backup under Time Machine with Mojave

[Neophyte_FL]

Mojave is the last OS I'm aware of where you can easily retrieve individual emails. I discovered that the hard way after upgrading to Catalina on a different iMac. I've had no problem backing up or retrieving my Cox.net emails under Mojave using Time Machine. However, my G-Mail accounts don't back up. When I go into Time Machine, the folders for all my G-Mail accounts are empty. I'm running a 2019 MacBook Air with Mojave Version 10-14.6 loaded. Many thanks.