Thunderbird was designed for a single user. If there is a separate server you can configure as a drive to Thunderbird, you could have both copies point to the virtual drive, but such folders are not under any protection by Thunderbird and you're susceptible to various network issues. But it could work. This is NOT an Thunderbird feature, so debugging and maintaining this is not supported. Good luck.

My installation is for a single user (me). I will access my domain host email via Thunderbird on both my desktop and my laptop depending on which is available or more convenient. I am currently training my new installation of TB on my laptop; implementing rules, marking spam, etc. I was hoping the rules and spam designations would carry over to my desktop so I don't have to redo everything there. Is that possible?

I was hoping the rules and spam designations would carry over to my desktop so I don't have to redo everything there. Is that possible?

You could export your profile, which includes accounts, messages, address books and settings. That way you don't need to do it all over on your other PC. But there is no sync, so if you change something on one, you would have to manually do it on the other one too. Export your Thunderbird Profile Import settings and data into Thunderbird