There was a lot of poking with a multimeter, cutting things open, and feeling up wires - but it’s finally done. I found the issues that were keeping reverse lights from working on the Exocet.
1) There was a wire that had been pinched/broken - resulting in no power to the reverse switch on the transmission.
2) The wire that I thought was a reverse light (silly me, it was the right color and the in the right place, and alongside all the other lights) - was not. I traced the switch coming off the wire and found the right one.