Does shutting off traction control save fuel?

Hook up a professional grade scan tool to the vehicles computers an check for DTC'S diagnostic trouble codes , that will tell a professional mechanic what to check.

Yes sir u should have a button to remove traction control. Logo of sliding tracks. A light should come on yellow in u r cluster to confirm traction off. Traction will follow your accelerator pedal to maximum rpm

Traction control doesn't shut the engine off. It will shut off the ABS system. Which is for slipping and sliding. You need to have the codes read. You can get code readers fairly cheap now days. But the cheaper ones will not read the ABS system or any other. Just the engine.

Kindly check this site.
Traction control F1technical net

Pretty much tells you the system with the fault

Traction Control is embedded into the abs braking
system, so diagnose that using the codes you have,
same as any other obd codes you get

The Reduced Power could be another problem & it
cuts off fuel injectors to save the exhaust converter
from overheating & being ruined

TRACTION CONTROL: An enhancement of an existing ABS system that prevents wheel spin while accelerating on wet or slick surfaces. It uses the same wheel speed sensors to monitor wheel speed during acceleration, but requires some additional control solenoids and a pump to apply braking pressure to control wheel spin. The traction control system brakes the drive wheel that's starting to spin to shift torque to the opposite drive wheel that still has traction. Most traction control systems only operate at speeds up to about 30 mph. Additional control strategies that some traction control systems use to limit wheel spin include reducing the throttle opening, upshifting the transmission, retarding spark timing and deactivating fuel injectors.

Hope helps.

means the traction control module is bad. That light is suppose to come on when you lose traction to let you know the traction control is kicking in.

The Enhanced Traction System (ETS) is designed to limit wheel slip during acceleration. This objective is accomplished by cutting fuel to selected cylinders, retarding spark and upshifting the transmission. The EBCM monitors wheel speed slip through the ABS wheel speed sensors and determines the desired torque reduction needed to minimize wheel spin.
the wheel speed sensor may be bad

traction control should stay on and it should be a button on the dash somewhere (not sure where, my cobalt doesnt have one) but if it got shut off at some point its probibly just telling you its off becuase other than racing theres no reason to shut Traction Control off.

it runs in the back ground so to say it reads the same sensors the anti lock brakes do if it sees a problem it will wake up