I had a long mail written using reportbug but somehow it appears to have been lost :-(
I said that I have two Google Mail accounts setup with Icedove, one configured with 2FA and so using a single purpose password for login, and the other using OAuth2. Also, the first one is a proper @gmail.com account (actually, this) while the other was created at first with a third party domain for Google+/Google Hangouts usage but after time Google Mail services were attached to it, so it now has two logins, one with a third party domain and another with the configured @gmail new mailbox. The first account logs in flawlessly. The second one fails to login using both the n...@gmail.com login as the @gmail.com one. As other people suggested, I'm more inclined to believe that the issue relies on OAuth2.