I wouldn't come to the conclusion that "the GPS shuts down the data stream".
Think about what you are doing in that video. You are not restarting or resetting the Aera 660, but rather, you are breaking, then remaking the RS-232 link to the JPI.
This is a wild guess, but perhaps the JPI is getting over-run with data, shuts down data processing, then recovers for a short time each time you remove the data stream and restore it. You could better test this theory by leaving the Aera 660 snapped into its mount and running normally, and then opening/closing the transmit line to the JPI.
How is the Aera 660 output configured? Perhaps there is a better selection.
If you want to test the Aera 660, remove it from the plane and connect it to a PC running one of the many available programs that will show you that the ASCII NMEA data stream is not stopping.
Something else to check is to make sure that the Aera 660 case is not touching the gizzymo enclosure. If the enclosure is pushing on the Aera 660 and trying to push it out of its mount, the RS-232 connection between the Aera 660 and the mount could be poor. Does pressing on the Aera 660 restore the data stream?
Steve