That was my problem.
I fixed my issue by running the following commands:
openssl genrsa -out logstash-es02.key 4096
openssl req -new -nodes -key logstash-es01.key -out logstash-es02.csr -config es02.conf
openssl x509 -req -in logstash-es02.csr -CA CACert.pem -CAkey CAKey.pem -CAcreateserial -out logstash-es01.crt -days 900  -extfile es02.conf -extensions req_extAdding the -exfile es02.conf -extensions req_ext to the end of the x509 create solved the problem.
And Just to keep the full solution all in one post, here is the es02.conf again for the cert.
[req]
default_bits = 4096
default_md = sha512
distinguished_name = dn
req_extensions = req_ext
prompt = no
[ dn ]
C=US
ST=NY
L=Gothan
O=Example
OU=Batman Tech Support
emailAddress=devops@example.com
CN=logstash-es02.ec2.example.com
[ req_ext ]
subjectAltName = @alt_names
extendedKeyUsage = serverAuth,clientAuth
[ alt_names ]
DNS.1 = logstash-es02.ec2.example.com
IP.1 = 10.249.39.247