A lot of folks disable the SAI system by simply stuffing a marble in the rubber hose (part #5 in the diagram below) that goes between the SAI solenoid and the air box. Besides being way less expensive and much easier to install than the multi-part SAI delete kits, this also has the advantage of not needing additional resistors to prevent pissing off the ECU (since the SAI solenoid remains in place). It also has the benefit of stealth in the event you need to have warranty work done on your bike. Whereas the SAI delete kit would be visually apparent to a Triumph technician, blocking off the air intake hose wouldn't be. So no worries about denied warranty claims due to unauthorized modifications.
I did this mod on my Thruxton because I was hoping to slow the rate at which the stainless exhaust headers turn brown. I like the gold color, but with the SAI active, gold turned to dull brown pretty quickly. After blocking off the SAI air intake the header pipes have so far stayed a pleasing light gold color. The popping in the exhaust on overrun never really bothered me, and I don't notice much difference with SAI disabled. It's probably somewhat less prevalent, but it's definitely still there. Might have more of an effect if you're running an aftermarket or modified exhaust system (mine is still bone stock).
Instead of a marble to block off the airbox hose, I decided to use a rubber vacuum cap like the one shown by the second image. I know lots of people have used a marble with no ill effects, but I had visions of a slippery glass marble migrating along the length of the hose. A rubber vacuum cap inside a rubber hose is about as high a friction coefficient as you're gonna get, so I'm not concerned about it moving. And it was $0.89 at Autozone as opposed to the $5 bag of marbles from Target.
So my suggestion would be to try blocking off the SAI airbox hose first to make sure you get the benefit you're looking for. If not, removing the obstruction from the hose would take all of 5 minutes and you're back where you started. If blocking the hose gives you the result you're looking for, then you could install the high-zoot kit instead if you like that better. Or you could just leave the hose blocked off and sell the kit to someone else
By the way, the kit doesn't need a gasket because the reed valves (part #3) serve as the gaskets.
Good luck with whichever way you decide to go.
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