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 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.