The names of accounts in eM Client are only informative (and set by the user when setting up the account). If the Google account authentication pops up and you login with a different email address than the pre-filled one then it will happily synchronize the account you log in despite the name in eM Client being different.
Right, so Bob’s eM Client account named gsacontitutioncouncil is syncing to his rwpeck59 GMail account. That is why I said the account must be setup more than once.
Therefore removing them both and adding them again will solve the problem.
Thank You Gary, You’re a Genius!
Tonight I looked in the gsaconstitutioncouncil account and discovered it had all the same folders and messages as my rwpeck59 account - exactly duplicated. It hadn’t occurred to me to look at that account since I haven’t used it in over a year. I just now deleted that account and everything is back to normal.
I realize now what happened. The reason I was confronted with two Google login windows is because one was for each gmail account, but I had pretty much forgotten about the gsaconstitutioncouncil account and was distracted doing other things at the same time, so I just mindlessly clicked to approve each. Unfortunately, I approved both using my rwpeck59 credentials so both eM Client accounts ended up syncing with the same gmail account. If I ever want to setup the gsaconstitutioncouncil account again, I’ll be alert to make sure I’m logging in to each account with the correct credentials.
Sorry to have bothered you all with my mistake, but hopefully it will be a resource for someone else who makes the same mindless mistake in the future.
This is good news! Filip to the rescue. 
Bob, I am sure your explanation will be invaluable to others. I am not a GMail user, but I can imagine how easy it is to click the approve button without fully reading what it is asking. I think we have all done that before in similar situations.
I’m having exactly the same issue 18/05/2021.
Deleted the gmail account from eClient (HilfordElectrical @ g mail com), then sent that same deleted account an email from another account (HilfordJames @ gmail com) and wammo, the email came in through a completely different gmail email account in eClient (BagpipesNZ @ gmail com), when I looked at this account in eClient none of this accounts folders existed and instead all 80% of the folders from HilfordElectrcial @ gmail com were under BagpipesNZ @ gmail com.
So I deleted both accounts from eClient and the problem has been solved.
Strange thing is I’ve not added or deleted any email accounts over the past 6 months!!!