Tonight I continued working on the periscope wire-up.
The periscope lighting kit includes pins for soldering to the main periscope board, as well as the controller board. I cut a 5-segment piece of connector, and bent it at a 90 degree angle, in preparation for attachment to the main periscope board.
I soldered the connector in from the inside of the main periscope board.
Rather than go with another 5-pin plastic connector, I picked up some single-pin jumper wires with connectors built in them. I soldered these onto the side of the wires opposite the existing 5-pin plastic connector, and slipped them over the pins on the controller board connector, with the 5-pin plastic connector having been moved to the main periscope logic board.
I still don't think that 5-pin plastic connector is going to cut it, the connections are flaky.