Your parts are actually from a Thunderbird pillion backrest basically identical to the Touring Longhaul but possibly a different vinyl color or texture.
Touring Backrest Pad, Passenger - Triumph THUNDERBIRD STORM | Triumph THUNDERBIRD STORM Touring Backrest Pad, Passenger supplied next day (UK only) by Fowlers Parts
It is definitely NOT a rider's backrest pad.
It is similar in every way to my R3 Touring Longhaul pillion backrest pads except you are missing the backing plate #4 in image A9750688.
And the kits come with the metal Triumph badge as well.
You have parts #2 and #3 in parts diagram below.
The plate is still available from Triumph Dealears worldwide on order from UK and I can get one from an NOS source as well.
Thunderbird, America version
R3 Touring version
Longhaul Passenger Backrest Pad Kit - Triumph ROCKET III TOURING | Triumph ROCKET III TOURING Longhaul Passenger Backrest Pad Kit supplied next day (UK only) by Fowlers Parts
