We currently run a single proxy server and I would like to setup a second
proxy server for failover purposes.

Now, I know I can setup 2 servers and just point DNS name (proxy) to a
single IP address. This allows for an Active/Passive setup meaning one is
always running and the other is just waiting for requests. If the primary
server fails, someone modifies DNS and the second server takes over. This
means it requires manual intervention to prevent a downtime.

What I would like to get is to have both servers as active. That way if
one fails, there is no manual intervention required to prevent downtime.

One suggestion was DNS round robin so that it just passes requests to each
server. Is this the best scenario, or what would be the best scenario?

I understand what ever solution I provide the cache volumes are still
independant for each server. All I am looking for is to make sure
connection is available if one server fails.