Request, Response and Headers JSON strings are already available in the tracer.
Whenever OOTB activity Rule-Connect-REST.pyInvokeRESTConnector runs, you can take a look at the parameter page in the clipboard and there you will find properties pyRequestHeaders, pyRequestData, pyResponseHeaders and pyResponseData.
I believe you are calling it via an activity, if so, if you trace the activity you should be able to see it in the tracer. Just enable the Data Page settings on tracer and then run and trace the activity. You should be able to see the raw response at Connect-REST step.