Hmm... how about in Keychain? Anything in there from that account you could delete?
I added an edit to my last post, having some success in getting rid of that annoying popup message from the message app on reboot, and then I tried to open the accounts tab in the preferences of the message app again. I swear it had no account listed when I did that the first time, but now it has that old Apple ID account listed! I cannot delete that account, it just won't do it. However, there is a check box for "Enable this account", which I immediately turned off, so now that account is not active. Tried to set up a new (modern) account and that new account gets set to a default type labeld "Jabberer". Sounds like a line from a Star Wars spin-off!

But it still won't let me delete the original old Apple ID account.
Now that annoying pop-up message does not appear, so we're closer, but somehow I get a log-in "password please" screen on wake from sleep on the MacBook Pro only. Where did that come from? I finely found the preference for that in the Security preference pane and turned that off.
I also used Onyx to delete all of the caches and reboot.
I am sure I should eventually do a clean install, but the thought gives me shudders, as it would take a whole day at least, and just to get rid of an old non-existent Apple ID in the Message preferences, doesn't sound worth it.

One more edit:
Eventually, considering that this computer is an older model, and I use it only as a backup machine, I reverted to an archived CCC backup of Sierra, 10.12.6, which seems rock solid. At least it has no "Jabberer" episode!
