The above articles are two references to issues when setting up GSUITE as a mail server in Eclipse. The following are a few troubleshooting steps I've taken in the past:
1. Setup Eclipse Server Configuration to have smtp-relay.gmail.com as the mail server.
2. Make sure the email addresses above the mail server setup are correct.
3. May have to unblock ports on router/firewall.
4. You will need to use credentials set by the app key.
5. Turned off SMTP authentication.
6. Added outside IP address to accept only from certain addresses.