How to get connection duration metric from logs for AppSync subscription?

If a user starts subscribing to a channel through a GraphQL subscription API on AppSync, how do we get the connection duration metric from the starting of subscription to the end of subscription? I have been trying to get the metric from AppSync logs by enabling ALL Field level logs with Verbose but couldn't find the metric. If I get it, I can calculate the total connection minutes for which the charge is being put on using AWS AppSync ($0.08 per million minutes)

In addition to that, how do we get the information about the messages being sent and received in the subscription?