I was able to resolve the conflict by going back to the rpm 2.24 version after manually removing 3.101. Certainly not ideal! However, I am constrained by the work environment where these hosts live. Here are the steps to resolve. Please note: Moving packages backwards is not ideal. I'm being forced due to compatibility issues between rpm installed Perl and the needs of Bugzilla.

cd /usr/local/lib64/perl5
tar cvf /var/tmp/perl5_Template.tar Template
mv Template.pm Template.pm.3.101.notused
yum install perl-Template-Toolkit
[download]

Update 7/20: While I show tar being used for backup, my copy-paste here neglected to show the removal of the Template directory. Sorry about that.