The HTTP Client session is using the wrong SSL protocol and/or cipher.
The 3rd part API requires the following session params (see sslc outptu):
Protocol : TLSv1.2
Cipher : ECDHE-RSA-AES256-GCM-SHA384
The ABL client normally checks a default list of ciphers which contains: DHE-RSA-AES256-GCM-SHA384.
This list can be seen in the cert.client.log when enabling SSL Debugging (article 000011391
But for the 3rd party API service the required cipher is slightly different as it contains an extra "EC" in front.