Client is unauthorized to retrieve access tokens using this method Gmail API C#

The service account needs to be authorized or it cant access the emails for the domain.

"Client is unauthorized to retrieve access tokens using this method"

Means that you have not authorized it properly check Delegating domain-wide authority to the service account

FWIW, since I'm too new to comment, DalmTo and Shane's answers pointed me in the right direction for my problem, which was that new functionality that I had added to an existing script (PHP) needed authorization of additional scopes for the service account. In my case, I working with the GMail API.

Besides the path mentioned in the Google documentation page that Shane cited, you can also go to https://admin.google.com/ac/owl/domainwidedelegation, where you can manage domain-wide delegation in a slightly different interface (I actually prefer it). I got to that page via Security > API Permissions, then clicking on the notice about those settings moving to App Access Control, where there's a "Manage Domain Wide Delegation" link at the bottom.