I just looked at some of my code that successfully uses private keys (for signing). And found code like this:
use File::Slurp qw(read_file);
use MIME::Base64 qw(encode_base64);
require Crypt::OpenSSL::RSA;
my $key_text = read_file( $key_filename );
my $rsa_key = Crypt::OpenSSL::RSA->new_private_key($key_text);
$rsa_key->use_pkcs1_padding();
my $bin_signature = $rsa_key->sign($plaintext);
print encode_base64($bin_signature, '');
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