Automatically detect and maintain account settings is grayed out

I would remove your Gmail account in System Preferences > Internet Accounts.
Make sure the account is removed from Apple Mail.
Quit Mail
Check in your User's Library/Mail/V3 folder and make sure the Gmail account has been removed. If not delete the folder. (Note: accounts have numbers now not the names as prior versions of Mail. You might need to look inside the folder to identify which is your Gmail account)
While you are in the V3 folder, look in Mail Data folder. Delete the 3 files that have Envelope in the name.
Next in your User's Library/Containers, move the com.apple.mail folder to the trash.
Open Mail. It will reindex your files.
Add Gmail account. It will download all messages from server. If you need to do any cleanup, I would do this first in your browser. Pay attention that your Inbox doesn't have thousands of messages. You might want to archive all to the All Mail folder. Move back only the latest emails to the Inbox.