[exim] Encrypted SSL connection to remote PostgreSQL cluster

Howdy!

Before I spend too much time trying to figure this out, is it possible to configure my PostgreSQL connection to use passwordless certificate based authentication?

Using am Exim configuration parameter such as (with appropriate pg_hba.conf settings on the PG end)
hide pgsql_servers = 192.168.45.16/exim/thepguser/<thepassword>
does work. For instance this works fine:
exim -be '${lookup pgsql{ select generate_series(1,10) }};'

I can connect without a password using the psql client, by passing a connection URI scheme, such as this:
psql "dbname=postgres \
host=192.168.45.16 \
sslcert=client.crt \
sslkey=client.key \
sslmode=verify-ca \
sslrootcert=root.crt \
user=thepgbuser"
But I see nothing in the Exim documentation that gives me much hope for Exim. I suppose another option, if possible, would be to export the relevant $PG* environment variables if Exim can somehow be told to use them?

Thanks!
Pat

PS, please CC me on replies as I am not subscribed to the ML