Error console had a message about "server certifications" having the same number.

What is the exact error message? What number?

He suggested I delete both accounts from Thunderbird and re-install them.

That's not necessarily good advice, as it makes your existing mail inaccessible.

Now Thunderbird will not allow me to re-install either account as a pop account.

Care to mention what prevents you from re-installing the accounts?

Also see https://support.google.com/accounts/answer/6010255?hl=en

Sorry -- don't remember the exact error number, and now they've all disappeared since I deleted the accounts.

As to deleting the accounts, hindsight is pretty much useless in this situation.

When I try to re-install, I get this error message in the advanced config page: "Thunderbird has failed to find the settings for your email account."

The error console says: Source file: resource:///modules/errUtils.js Error: an error occurred during a connection to pop.gmail.com:995. You have received an invalid certificate. Please contact the server adminstrator or email correspondent and give them the following information: Your certificate contains the same serial number as another certificate issued by the certificate authority. Please get a new certificate containing a unique serial number. (Error code: sec_error_reused_issuer_and_serial)

As to "Also see https://support.google.com/accounts/answer/6010255?hl=en", I have already done that too, and it is set for allowing less secure apps. I had to change that setting when I first started using TB.

Error code: sec_error_reused_issuer_and_serial

How do you connect to the Internet? Is this a corporate network? Do you use a proxy? Is a proxy configured in Thunderbird? What security software do you run (anti-virus/firewall)? Did you scan your computer for malware? Can you access secure sites with your browser? If so, what is your browser?

How do you connect to the Internet?

At work I connect to the university wifi via eduroam. At home I use my cellphone as a hot spot and connect via wifi. The problem is the same on both networks.

Is this a corporate network? The cell phone is GCI. The university network could be considered corporate, I guess. In any case, the problem is the same on both.

Do you use a proxy? Is a proxy configured in Thunderbird?

Just smtp, ssl, which the google server specifies. I don't think I've ever set one up.

What security software do you run (anti-virus/firewall)? Did you scan your computer for malware?

AVAST Mac Security 2015. Web shield is inactive right now. The program is supposed to be actively scanning in real time, but I just ran a scan, which shows no infections.

Can you access secure sites with your browser? If so, what is your browser?

Yes, I can access secure sites. I use Firefox and Safari.

See https://wiki.mozilla.org/Thunderbird:Testing:Antivirus_Related_Performance_Issues#AVAST

https://wiki.mozilla.org/Thunderbird:Testing:Antivirus_Related_Performance_Issues#AVAST is actually specific to TB 2016 and Windows, but with this clue I found https://www.avast.com/faq.php?article=AVKB72#idt_11, which solved my problem.

Thanks.