Esp stays on when the car is in drive or idle

You can clear codes until the cows come home, but if you don't fix the underlying problem, the light will come back on. Get the codes read. That's your starting point

yes

the operators guide shows what these mean and what to do.
lost that>? i have one, and 08 JK.
pages 105 to 116
it resets each drive. the opr guide says that, and does.
its a very complex system, you should RTM.

ill quote your missing pages.
ABS:
If the light remains on after start-up or comes on and
stays on at road speeds, it may indicate that the ABS has
detected a malfunction or has become inoperative. The
system reverts to standard non-anti-lock brakes.
ESP:/TCS
The ESP/TCS Indicator Light (located in the instrument
cluster), starts to flash as soon as the tires lose traction
and the ESP system becomes active. The ESP/TCS Indicator
Light also flashes when TCS is active. If the
ESP/TCS Indicator Light begins to flash during acceleration,
ease up on the accelerator and apply as little throttle
as possible. Be sure to adapt your speed and driving to
the prevailing road conditions

is this clear? if not ask more, questions , more specific and we can peel the onion deep as you want.
also wiki this topic, to understand it ...

location not stated, or road conditions. nor if in 4low , nor if the ESP switch is off or on. Ask Suzuki for help (lol) or any ASE shop.

it's not magic, it can not give traction , if none.
on ice slow down. (esp can do that too. slow you,brake you and even
shift gears in the transmission)

are you in 4wd? or high 4Low, esp is inactive. (or limited)
read the operators guide. (if lost, get one now)
read the page on driving on ice.
chapters 5,6,7.
have you had any off these conditions , related to ESP, this a
is the ESP light acting wrong, or CEL check engine light running?
are all dash lamps (warning) showing correctly per the opr. guide?
ESP & ABS are vary complex, (not magic)


quote from the servise manual. (car battery dead or disconnected?)
ESP control module
When ESP control module is removed / installed, do
not use impact wrenches which generate shock or
impact to avoid damaging sensors in ESP control
module.
Note that Calibrate word here..!
When any of the following operation is done, calibrate
steering angle sensor, G sensor and master cylinder
pressure sensor (in ESP control module) referring to
"Sensor Calibration in Section 4F
- When battery or dome fuse is removed. (a low battery or weak)
- When steering angle sensor is replaced.
- When ESP control module is removed.
- When yaw rate / G sensor assembly is removed.


read this, it covers this system well,

http://www.wkjeeps.com/wk_esp.htm

read page 7-2 here (the do not drive words)
http://www.autodealertools.com/quickQuote/manuals/2007/Grand%20Vitara.pdf

this car has no center differential. (read limits there of)
are you using chains on the tires?
oper guide page 4-6 , read that yet?

If the vehicle speed is greater thanapproximately 30 km/h (19 mph), the ESP systems (other than ABS) will turn
on automatically and the light will go out.
• When the transfer switch (if equipped) is
turned to the "4L LOCK" position, the
ESP systems (other than ABS) will be canceled automatically. The light will come on and stay on.
• If the ESP systems operate continu-ously such as when driving on slippery roads, the traction control functions of the ESP systems may be canceled temporarily to avoid overheating the brake pads, and the light will come on. After a short period of time, the ESP.

(this latter cut out happens, with wild driving)

The light is telling you that there is a problem in the engine management system. Have the fault codes read and fix the faulty sensor/servo

sorry but you could have a side light out but you will need to visit the dealer to clear the faults

Sometimes the issue is with the mechanical vacuum pump off to the side of the ABS/ESP module. It looks like a round silver canister. This issue is all over Google with many possibilities but the one I copied is most common.

I had the same issue with my '05 A4 1.8T.  Turns out it was the RPM sensor.  Audi tried to tell me it was teh fuel pump and the cam-shaft positioning sensor.  Paid for teh fuel pump replacement and it died 6 blocks from the dealership.  Then they replaced the RPM snesor, works great now... Except it's still an Audi.

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

The Throttle Body Needs Basic Settings To Be Carried Out