With the JRE installed by BE installation, even with JCE applied properly, ECDHE cipher suites are not available. e.g.

2019 Feb 19 12:03:08:312 GMT -8 testACQPCommand Debug [main] - [root] Ignoring unavailable cipher suite: TLS_ECDHE_ECDSA_WITH_AES_128_CBC_SHA256
2019 Feb 19 12:03:08:312 GMT -8 testACQPCommand Debug [main] - [root] Ignoring unavailable cipher suite: TLS_ECDHE_ECDSA_WITH_AES_256_CBC_SHA
2019 Feb 19 12:03:08:312 GMT -8 testACQPCommand Debug [main] - [root] Ignoring unavailable cipher suite: TLS_ECDHE_ECDSA_WITH_AES_128_CBC_SHA256
2019 Feb 19 12:03:08:312 GMT -8 testACQPCommand Debug [main] - [root] Ignoring unavailable cipher suite: TLS_ECDHE_RSA_WITH_AES_128_GCM_SHA256
2019 Feb 19 12:03:08:312 GMT -8 testACQPCommand Debug [main] - [root] Ignoring unavailable cipher suite: TLS_ECDHE_RSA_WITH_AES_256_CBC_SHA
2019 Feb 19 12:03:08:313 GMT -8 testACQPCommand Debug [main] - [root] Ignoring unavailable cipher suite: TLS_ECDHE_RSA_WITH_AES_256_GCM_SHA384

Those ciphers are available with standard alone JRE installation, or with JRE installed with BW installation.

Cause to the issue:
The Java classes are packaged into the signed sunec.jar in the JRE extensions directory and the native functions are packaged into libsunec.so or sunec.dll or libsunec.dylib in the JRE native libraries directory. When this native library is not present then fewer algorithms are supported.

Switch be-engine to use the standard JRE

Option 2:
Copy the missing native library(sunec.dll(Widonws)/libsunec.so(Linux)/libsunec.dylib(Mac) ) from the JDK installation(under bin folder for windows, and lib folder for Linux/Mac) and placed into same folder under tibcojre.