Most chassis parts are not interchangeable with the other Rockets. The assumption should always be that if it's a Touring, you need specific bits. Then you can be pleasantly surprised sometimes.
Four Triumph parts I'd recommend
World of Triumph - they have all the parts "fiches" online and you can just go find what you need. Generally they ship quickly (most recently I needed a chrome "button" to cover the seat fastening hole in the fender and the black plastic cover that covers the electrical wires and cables up by the frame neck... had them within a week or so. I got a bit uh impatient wedging that plastic bit back on last time I disassembled and cracked it.
Triumph Motorcycles | triumph-select-model-part | Triumph Parts | Triumph Clothing | Triumph Accessories | Triumph Bike Rocket III Touring | Side amp Infill Panels - and wow, I wonder what the heck that 1500 euro panel is.
That page also lists the grommets. I also slathered clear silicone around mine and glued them into place, it's very easy to push them in otherwise when replacing a panel. One grommet missing will lead to the panel flapping around and potentially flying off.
I'd also recommend drilling a hole through the rearmost stem of the side panel (the one that sticks out in the middle of the infill panel) and threading a ziptie through that and then closing the ziptie around the bike frame. That way, if the panel comes off, it will still be tied to the bike. Saved me having to buy one new panel already.