The a/c was fitted I believe with Satcom which can be used in real time to send back engine data etc or used as a Satphone. The data stream costs money and was not subscribed to by the airline however the Satphone was still available for use in an emergency & only cost the airline money if used.
The pings I believe were just the handshake, similar to your mobile phone, & were produced to establish a connection if needed. I have been wondering if the final "partial" ping was in fact generated when the power went down on the Satcom & was re established by the RAT say. ie maybe the system was trying to re establish contact after a power outage.