Check this post form 2014 - https://www.k1600forum.com//forum/bmw-k1600-lighting-electrical/50306-add-power-trunk.html
Here's the gist of the connector detail ( assuming you are talking only the Top Case )
"""I haven't given up on the idea of adding pins to the BMW connector. I finally tracked down a solid lead on the exact parts needed. It's a connector made by Kostal. The site I found the info on is foreign, but I was able to navigate it well enough to figure out the exact parts. They don't have online ordering, so if another source can't be found it will take some phone calls. If anyone has some inside info on where parts like these could be obtained in small quantities in the US please let me know!
Web site I found info on: TGS Onlineshop
Female connector from trunk cable:
Part# 09 4310 02
Pin type: "LKS 1,5 socket" (also called buchse on the site)
Tools for insertion/removal: R701 and F425
(not sure what F425 is for)
Male connector from bike:
Part# 09 3310 02
Pin type: "LKS 1,5 stift"
Tools for insertion/removal: R775 and F425
(note, female uses R701 and male uses R775) """"
I have a "flasher" on order and want to use connectors as well but I'm thinking the rear tail light AND the Top Case. That way if the case is off ( the way I ride daily) I'll still have the flashing...