They also sell replacement springs on eBay. This listing also has the correct unloaded spring length spec.
Cam Chain Tensioner Spring Kit - Triumph Rocket III | eBay
Price: GBP 14.95
Approximately US $20.30
Replacement Cam Chain Tensioner Spring Kit for Triumph Rocket III
(Stock Ref Z585)
Replacement Cam Chain Tensioner Spring complete with copper sealing washer.
It is recommended that the spring is replaced if its length has reduced significantly below
73.7mm. This is a much more cost effective option than replacing the complete tensioner assembly.
Replacement of the spring requires only the 19mm hexagon headed bolt to be removed and the spring can then be replaced. A very simple job.
Fits: 750/900Trident, 750/900/955/1050 Speed Triple, 750/900/1000/1200/955 Daytona, 900/1200 Trophy, 900/955/1050 Tiger, Thunderbird 900, Thunderbird Sport, Legend TT, Adventurer, Rocket III, Rocket III Classic, Rocket III Roadster, Rocket III Touring, Sprint 900, Sprint Sport, Sprint Executive, Sprint ST 955/1050, Sprint RS
There is also the ridiculously expensive
25% off US$67.46 plastic gauge
tool T3880068 going discounted on eBay at the moment for the check and add slug to load spring if short.
Remove Centre Nut