Perl DBI takes 60 seconds to connect to an Oracle database, every single time
Thanks to @ThisSuitIsBlackNot for pointing me to the tracing functionaility in DBI, I was able to track this down to an error with not specifying port.  I knew that I should be pointing at 1521 when setting up other connections in other programs, but DBI didn't require port to function, it was just 60 seconds of waiting for it to give results.  DBI assumes 1526 to be the target port first unless told otherwise, so when targeting a server running on 1521, it was timing out after 60 seconds before trying 1521.

Original:

DBI -> port 1526 -> no response -> wait 60s -> no response -> fail -> port 1521 -> success

Specifying port:

DBI -> port 1521 -> success