No unfortunatiely this will never fit a Touring R3T it is for R3 standards, Classics and Roadsters only.
This is a
CLASSIC TOURING SEAT - DUAL A9708164
For use with ADJUSTABLE RIDER BACKREST A9708160
There is a Touring version - actually 2 versions a solo with seperate copillion and a dual Longhaul version.
What you are after is either
LONGHAUL TOURING SEAT - DUAL A9700209
Shown with ADJUSTABLE RIDER BACKREST - LONGHAUL A9708158
or
BUCKET SOLO SEAT A9708162
Shown with ADJUSTABLE RIDER BACKREST - LONGHAUL A9708158
and maybe
COMFORT PILLION SEAT A9708163
The backrests are ALL interchangeable except the Touring one is a grayer color vinyl hence the slightly different part numbers.
There are still the base seats available new or used with the hole for the backrest but rarely from dealers now. A few of us have made our own backrests to suit the square hole and mounting mount. Others just get a 'Utopia USA' brand backrest. The seats with or without the hole and or riders backrest, are typically the most comfortable factory Triumph seats available.
I can source both the Touring base seats and pillion but no longer the rider's backrests.
The backrests are the 'unicorn' bit. The used sets come up sporadically, none for 6 months then a couple in a month then 12 months zilch.