Timeout if connection is lost (OpenVPN)

I am connected to a PostgreSQL server via OpenVPN.
I have an open connection that sends a select statement every 10 seconds in a loop.

If the OpenVPN connection closes due to some network issue, the next select statement takes 3min+ until a timeout appears.

Question:
Is there any elegant way of handling such a scenario and get an appropriate quick timeout response?
I have tested pgconn.checkConn(), but checkConn() tells, that everything is fine altough it isn't because OpenVPN connection has been gone.

Start by examining pgconn.checkConn() and reproducing the reported loop against PostgreSQL while disconnecting OpenVPN. The issue does not identify a file, test, timeout setting, or expected implementation, so the appropriate quick-timeout behavior would need to be clarified before defining completion.

Written by the indexing model from the issue text.