if you have a lot of email you can expect the initial download to take a long time as Google to limit your daily data downloads. Once the download limit is reached then things stop for 24 hours. these limits are for gsuite, I would expect free accounts to be somewhat lower. https://support.google.com/a/answer/1071518?hl=en

Sometimes just visiting this link and following the prompts will get it started again. https://accounts.google.com/b/0/DisplayUnlockCaptcha

That seemed so logical! but nothing changed. I followed the prompts, and Thunderbird looked for new messages... and informed me that there were no new messages. I've also attempted to make Mail my POP message downloader, and it can get all the current ones, but I can't seem to change it from IMAP.

I've kept Mail closed, and even made Thunderbird my primary email, but the result is still the same. If it's helpful, I have 88,000+/- msgs on Gmail, over 3 em accts, plus calendar and voice. Thunderbird has stopped at 57704. (Yes, I do indeed need to sift down and delete, but Gmail has such awful sorting choices. I'm on a Chromebook at work so you can see the problem.

Thank you for the suggestion though, it seemed like the perfect answer.

re :I've also attempted to make Mail my POP message

Did it actually download any messages to 'Mail' ? Is it running in the background? Open Mail to see if newer emails are in it.

Gmail will not allow a popped message to get re popped, but there are some workarounds.

Read info: eg: 'recent mode' and 'Re-downloading messages and excluding existing messages' https://support.google.com/a/answer/6089246?hl=en