The factory accessory riders backrest have not been available from delears for quite a few years unless they happened to have old stock on hand. About the only chance of finding one now is second hand although the Classic seat like yours but with a square hole and plug to suit are still available and have been highly discounted in Australia and the UK for years for about Au$170 (US$132) - you do not see them discounted like this in the USA for some reason.
If you want the Triumph factory version I posted one on eBay UK currently a couple of days ago, and it is still there today. TRIUMPH ROCKET TOURING SEAT & RIDER BACKREST & BRACKET CLASSIC ROADSTER NO/3476* | eBay
You can also get a riders backrest by purchasing from Utopia who have a model to suit the the R3 Standards Solo riders seat and separate pillion seat. These will fit the Classic as well. Need to check re a Classic dual seat version.
Utopia Products - Motorcycle Driver Backrest - Motorcycle Seat
If you just want to use it as a solo you would have to get a rear pillion seat bracket and trim off the back end and pad or make your own bracket to suit.
From a recent post of mine here:https: //
www.r3owners.net/threads/any-rider-backrest-and-trailer-hitch-available.32004/#post-503276
Plenty of threads if you search or look at the 5 related threads posted below every thread.
This
eBay listing is for the fairly rare factory solution that came out with the early Standard R3 as an option and was stock with some Classic 'Tourer' models up to 2008. It was then available as an accessory until they stopped manufacture of the back rest unit they source from and external supplier who was charging them too much it is assumed.
It also fits Roadster models. The seat is the one piece dual seat like yours but has a square hole for the rider's backrest with a plastic plug when backrest not fitted. That seat also has an unplugged version without the hole but the holey version has been on sale in the UK and Australia for years now for around AU$172 (US$130). The backrests have been unavailable from dealers for years but occassionly turn up - I have had 3 with seats so far.
The next options are aftermarket seats and back rests like
Corbin or just get the backrest to fit to existing separate solo and pillion seat combos like the
Utopia branded ones.
Some of us have made our own
rider's backrest, like me.
If you search the forum for threads wioth the words in Bold above you should find it all.
Australia eBay
TRIUMPH ROCKET TOURING SEAT & RIDER BACKREST & BRACKET CLASSIC ROADSTER NO/3476* | eBay
USA eBay
TRIUMPH ROCKET TOURING SEAT & RIDER BACKREST & BRACKET CLASSIC ROADSTER NO/3476* | eBay