You might be able to work around this by upgrading OpenSSL and then updating/reinstalling Net::SSLeay (the XS bindings to OpenSSL) from CPAN. You will probably also need to upgrade Net::SSLeay to a version that supports the newer OpenSSL. That should get you TLS 1.2 support, but if you are still running a 19 year old perl, you probably should be looking at a forklift upgrade here and planning to migrate the whole application to a new system.
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