I added the brake light to the BMW top box I added to my GT. I wanted the flash at brake option. I utilized a GS-100A module. I didn't splice into bike's harness. I spliced into the top box light's leads. These things are a couple bucks on ebay. Give it a google if you want...it's worth a google. The light acts as normal, except when the brake is applied, it strobes before turning solid. I don't know how your GA top box light functions or how or if it's wired differently than the harness of my GT. I just plugged the box in to the connector under the seat and the central locking etc worked. The connection for the brake light was already wired and ready to go in the lid when I added the light a few months later. Best of luck to ya!
‘18 K16GT Option 719 Blue Planet Metallic with matching BMW top-box, Bomber Brown RDL, Denali D7s, Ilium f&r bars with highway pegs
IBA # 63673
‘14 FJR-ES Candy Red (sold)
‘83 CB1100F Blue White & Red (in a garage);
‘83 CB1100F Red White & Black (in a shed);
‘76 CR125 Elsinore Red (sold);
‘73? CB125S Torquoise (sold)