I don't have handy a picture of the rear of the FJR, but here's the back end of my ZRX1100LT (heh) with the same topcase I might use on the FJR. Also visible is the strip LED brake light (Amazon) only on the rear face of the Givi topcase mount.
The trunk has simple, inexpensive strip LED lighting (EBay), connected to the tail and brake circuits via a little diode-and-resistor "controller" I picked off this forum long ago (I think). So it goes dim and then bright when the brake light switches are activated.
I chose not to go to the trouble of hooking up turn signals to the trunk. On the ZRX, I have a Givi sidecase setup now that has the old Wingrack with turn signals included (not shown in this older photo).
You're looking at about 2 hours of work and less than twenty bucks of stuff, even including the diode/resistor pack.
Possibly not the solution for everyone but something to think about.
2020 Ninja 400 in the hands of the Missus
2004 Suzuki SV650S, also Hers
In the avatar: 1966 Velocette Venom Thruxton and 1967 BSA Royal Star.