Postgres - Enabling certificate authentication (no password)

Installation/Setup
1

I was able to successfully connect my Kong deployment (GCP GKE) to a Postgres database (GCP Cloud SQL) using the following, basic configuration:

database: "postgres"
pg_host: "my-database-host"
pg_port: "my-database-port"
pg_database: "my-database"
pg_user: "my-database-user"
pg_password: "my-database-password"

I then enabled SSL in the database, created a client certificate for my Kong user and added SSL-related properties to Kong config, ending up with the following:

database: "postgres"
pg_host: "my-database-host"
pg_port: "my-database-port"
pg_database: "my-database"
pg_user: "my-database-user"
# pg_password: "This is commented out"
pg_ssl: "on"
pg_ssl_required: "on"
pg_ssl_verify: "on"
pg_ssl_version: "tlsv1_2"
pg_ssl_cert: "/etc/secrets/db-cert-secret/tls.crt"
pg_ssl_cert_key: "/etc/secrets/db-cert-secret/tls.key"
lua_ssl_trusted_certificate: "/etc/secrets/db-cert-secret/ca.pem"

Please note that the postgres password property is commented out - it would seem logical to me I can now omit the password since the authentication should now happen with the client certificate.

However, the connectivity now fails with the init migrations job throwing an error:

Error: missing password, required for connect
    Run with --v (verbose) or --vv (debug) for more details

Is there anything I’m doing wrong? Is certificate-based authentication supported by Kong?