Here's an old GSX-R Forum post that may be useful, a post from 'Motorhead' a fair way down describes a fault that resulted in a Suzuki recall with 2007 GSX-R1000 which the GSX-S has a relationship too as you know.
QUOTE: " The second is a defective (ISC) Idle Speed Control Valve. Suzuki has determined that all GSX-R1000K7 motorcycles are equipped with an Idle Speed Control (ISC) Valve that may not return to the correct start-up position each time the ignition switch is turned to the off position. Due to improper shape of the internal mechanism that moves the ISC valve, the valve may remain in the open position instead of moving to the
correct start-up position. This can result in no-load engine idle speeds as high as 5000 RPM’s the next time the engine is started. If you choose to operate the motorcycle in this condition, you may have difficulty operating the motorcycle, which could result in a crash.
Suzuki is recalling affected units for the installation of an improved ISC valve and Engine Control Module (ECM). The new ECM contains revised programming which controls the ISC valve functions related to idle speed. The ISC valve related ECM changes have no effect on overall performance of the motorcycle. Repair time is approximately 1 hour and will be done at no cost to you for parts or labor. "
I also saw references to O2 sensor replacements in the same bike that brought up C40 ISC code. Your's is C65, but there's 10 years difference. One Guy reported like you, the alarm just cleared by itself after a few days.
That based on the old post & my past readings online of Suzuki issues, could mean 2 things:
1/ a temporary mechanical stiffness just dislodged itself in the motor assembly actuator. (Older GSX-R750'S used to be prone to solder joints failing due to vibration. It was possible to pull it apart and re-solder . Cheaper than Suzuki spare prices)
2/ Learned Values will fix themselves with feedback from a working correctly sensor to the ECU, but with a lot more time than a few days.
Edit: Your observations of the - line for TPS is correct for a corectly adjusted sensor, so that's all good.
The STVA motorised actuator is a stepper motor that turns the ECU controlled secondary butterfly valves via the throttle body shaft. It is the automatic choke mechanism for the bike.
If it doesn't turn the shaft correctly, stays open, it makes the bike hard to start when cold, or stays closed, closes off the air way through the throttle bodies and strangles the motor. Or someway between the two.
There's quite a few Youtube on a repair on line.