Hi, I'm just about to install my old Autocom Active 7 Smart into my Sport. This has been on 3 bikes so far and is worth using again. There is a small tray space under the seat, between the tank and the battery. The Sport has a tool bag there which is only good enough as a paper weight, in the usual Triumph fashion.
I'm not familiar with the 1050 Tiger, but have the seat off and take a look.