Engine hesitation, the trac off light comes and car hesitates.

The electronics and modules will tell the reason. It sounds like a computer network issue. You need a mobile auto electrician with a pro grade scan tool computer.

https://www.google.com/search?q=mobile+auto+electrician+near+me

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run the fault codes
possible faults include the vacuum actuated turbo vane changer not changing according to the manifold vacuum, fuel pressure problems or faulty cat converter blocking exhaust

Has to be diagnosed at a repair shop

Surely you don't think someone without
the vehicle to test ,can guess at what is
wrong with it

I have a 01 pt that did the same thing. By you're exhaust manifold there is a thick wire set with loom over it. Pull it back and check the orange wire. It controls the crankshaft Senor mine was burnt through. Easy fix black tape and a price of wire, spliced it together and was good to go. But I relocated the wire off my exhaust

Your suspicion is correct. The trac light will come on when you have unevenly worn or tyres of different sizes on your rear wheels. What's more, this problem is equally caused by faulty rear shock absorbers, especially in bends or uneven surface.

What you have is brake debris in the sensor area. The hesitation is just the Traction control working. The Traction control is suppose to limit one wheel from spinning faster than the other. It does this by interrupting the engine and applying the rear brakes to the faster spinning side.

Most likely you have brake debris from the emergency brakes blinding the sensors. The rear E brakes are hidden from view and are actually small drum brakes inside the rear rotors.

time for sparkplug change, gas filter change

This is just a shot... Get a Can of "SeaFoam" and pour it into your gas tank with a full tank of gas. Then take it for a "Spirited" drive on the freeway or highway for at least 30 minutes to an hour. (Longer is better) i have had many cars with a little hesitation or sputtering fixed with this awsome product. it is a very powerful cleaner that has chemicals that other brands simply do not have. Conditions should have improved after your 1 hour drive. and will continue to improve as you continue to drive with that treated tank of gas. If the problem persists then you need to get the OBD trouble codes and let it direct you to the failed part. At least you would rule dirt "Out of the Question" (Also read the can for other things that Seafoam can fix on your car and how to use it) also does wonders for a couple cap-fuls in the lawn-mower...Chainsaw....Snowblower...etc i Hope this helps you out... Good Luck!

A week ago, on my Lexus ES 300 (2001), "Check Engine" and "Trac Off" lights came on. This coincided with me filling the gas tank to the brim to round the dollar to be paid. I cleaned the gas tank cap and the tank opening. However, both lights persisted. On the same day, when I turned on the car again, there was a hesitance, a stuttering to come on. Both "Check Engine" and "Trac Off" lights were still on.

The next day, the car wouldn't come on at all. It sounded as the battery was dead. I couldn't even jump start the car. So, I got a new battery from Costco ($59) and put it in. It took 15-20 seconds of cranking to get the car started. Once it was started, the engine sounded fine and the RPM normal. The "Check Engine" light was off. However, the "Trac Off" was still on. I cleaned the gas tank cap one more time.

The next morning, when I turned the car on, there was no problems. It came on instantly as it used to be, didn't have any warning lights, and drove smoothly.

Replace the camshaft sensor, the issue will go away.