I posted this once before but Triumph does have a part number for an adjustment tool. It's just a round piece that's the exact size to fit in the sleeve and has a right angle turn to it. I keep it in my tool bag on the bike.
The part number is: T2300995 and shown as "RSU Adjustment Tool"
It cost $3.00 and works fine. A screwdriver the right diameter with a cut off end (as mentioned above) might work even better.
