Have a vw touareg 2005, esp light stays on and car

Yes, it is a known issue

https://www.google.com/search?q=vw+jetta+2.0+tfsi+rev+hanging

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IF the light is staying on its because it has a problem kind of like a check light. Also if the light is on the ESP IS DISENGAGED. meaning no traction control and most likely no antilock brakes. You need to pull the codes from all of the computers in the car and find out why the system is shutting down. IE wheel speed sensor, loss of power, short to ground, mismatched tires, ride height sensors, etc

Whenever this warning light or any other stays on in the dash it is indicating that the systems control module (or the system sensor in the case of lights like low oil pressure, door open indicators etc.) has detected a fault, it then disables the system (this applies to ABS,TCS, TCM, SRS and BCM faults and others) as long as the light is on. You must now have the dealer hook up a special electronic diagnostic tool and "scan" the system for the fault code that is stored for the problem(s)

Legend of Abbreviations. ABS Antilock brake system.TCS Traction control system, TCM Transmission control module, SRS Supplemental restraint system, BCM Body control module

With the correct spares at hand the job should take no longer than a couple of days and no the gearbox should not have to be removed for only a water pump change.

when vw started to use the computer controlled gearbox system a criticism was the shift was very harsh,to counter this they made it rev slightly before changing.so that you know the system, try this out....without touching the gas.....put it in d and let the car accelerate to its max speed,stop,then use 1/3rd of gas (keep your foot still)and let it do the same...stop,then,if safe,put your foot to the floor,hard, notice when the car changes gear(revs/speed)then if you drive,only using the first1/3rd of the gas,the cars change pattern will alter to suit.......wierd it is.....

Change Glow plugs heater control module.

the esp light is caused by failure of the brake light switch in most models. check your brake light operation and replace the switch if the brake lights have failed. the switch is found in the footwell above the brake pedal

TOURAN OR TOUAREG ??ESP LIGHT ON?LET ME KNOW

VW engines intend to do this, even if you pull up at a set of traffic lights it will nearly cut out or go into high rev's. i have an a3 & once driving down the road @ about 50kpm, I lost power stearing for 1-2 seconds, stearing wheel went stiff. Audi are a good drive but needs lots of tlc. One other thing is fuel pump could be acting up a bit.

Sound's like it has gone into limp home mode to protect itself, try the audi /vw forum lots of knowledge there.