Post for googlers that stumble on the same issue - it seems that "overconfiguration" is not a great idea for Filebeat and Logstash.

I've decided to explicitly set ssl.verification_mode to none in my Filebeat config and then I got following Filebeat and Logstash errors:

filebeat_1  | 2017/01/03 07:43:49.136717 single.go:140: ERR Connecting error publishing events (retrying): EOF
filebeat_1  | 2017/01/03 07:43:50.152824 single.go:140: ERR Connecting error publishing events (retrying): EOF
filebeat_1  | 2017/01/03 07:43:52.157279 single.go:140: ERR Connecting error publishing events (retrying): EOF
filebeat_1  | 2017/01/03 07:43:56.173144 single.go:140: ERR Connecting error publishing events (retrying): EOF                                                          
filebeat_1  | 2017/01/03 07:44:04.189167 single.go:140: ERR Connecting error publishing events (retrying): EOF


logstash_1       | 07:42:35.714 [Api Webserver] INFO  logstash.agent - Successfully started Logstash API endpoint {:port=>9600}                                                                                                         
logstash_1       | 07:43:49.135 [nioEventLoopGroup-4-1] ERROR org.logstash.beats.BeatsHandler - Exception: org.logstash.beats.BeatsParser$InvalidFrameProtocolException: Invalid Frame Type, received: 3                                      
logstash_1       | 07:43:49.139 [nioEventLoopGroup-4-1] ERROR org.logstash.beats.BeatsHandler - Exception: org.logstash.beats.BeatsParser$InvalidFrameProtocolException: Invalid Frame Type, received: 1                                      
logstash_1       | 07:43:50.150 [nioEventLoopGroup-4-2] ERROR org.logstash.beats.BeatsHandler - Exception: org.logstash.beats.BeatsParser$InvalidFrameProtocolException: Invalid Frame Type, received: 3                                      
logstash_1       | 07:43:50.154 [nioEventLoopGroup-4-2] ERROR org.logstash.beats.BeatsHandler - Exception: org.logstash.beats.BeatsParser$InvalidFrameProtocolException: Invalid Frame Type, received: 1                        
logstash_1       | 07:43:52.156 [nioEventLoopGroup-4-3] ERROR org.logstash.beats.BeatsHandler - Exception: org.logstash.beats.BeatsParser$InvalidFrameProtocolException: Invalid Frame Type, received: 3                                      
logstash_1       | 07:43:52.157 [nioEventLoopGroup-4-3] ERROR org.logstash.beats.BeatsHandler - Exception: org.logstash.beats.BeatsParser$InvalidFrameProtocolException: Invalid Frame Type, received: 1                                      
logstash_1       | 07:43:56.170 [nioEventLoopGroup-4-4] ERROR org.logstash.beats.BeatsHandler - Exception: org.logstash.beats.BeatsParser$InvalidFrameProtocolException: Invalid Frame Type, received: 3                                      
logstash_1       | 07:43:56.175 [nioEventLoopGroup-4-4] ERROR org.logstash.beats.BeatsHandler - Exception: org.logstash.beats.BeatsParser$InvalidFrameProtocolException: Invalid Frame Type, received: 1

It seems it's better to stay quiet with Filebeat :) Hopefully this helped to resolve your issue.