You are missing HB taxiway. It is a entry point for the new Terminal 4 extension. Please look at latest JFK ground map published by FAA.
Also the jetway at gate 41 at terminal 4 does not move with default command of CTRL J. And no, AES not installed for this airport.
When selecting "nose left, tail right" off of gate 41 at the Terminal 4 extension, GSX will push the aircraft forever backwards all the way to gate 31 which is were a taxi line is located. If you put the HB extension in, please use a taxi line to connect to the one by gate 31 and fix the GSX issue.
