There may (or not) be a related item in google talk support:
Google Talk Help - Google Support
Official Google Talk Help Center where you can find tips
and tutorials on using Google Talk and other answers to
frequently asked ... Google apps. Main menu. Talk Help.
https://support.google.com/talk/?hl=en
Check Google's allow the Less Secure app setting; although
that may not be the cause of your issue in this regard...
Depending on the Mac and its Mac OS X version, the Message
feature may be located in iChat and not Messages. If this is, see:
How do I Change a Password on iChat
Oh, happened to note the other thread was yours after reply
was posted there; at least they're not same ones in both:
How do I get my text messages on my Mac Air
Sometimes you may have to go into the gmail settings in
the Mac (preferences?) ~ delete them, then renew them.
There are several articles online with issues of this nature
going back a few years; similar sounding problems, too.
Not sure if this would help. (Notice you accidentally clicked
the button and marked your unanswered thread 'solved'.)
Good luck in this matter...! 🙂