I wouldn't believe it or figured it out if I had not read this forum. When it warmed up a couple weeks ago I decided to check the air pressure in the tires in all 3 vehicles with my new SLIME air pump. Like every other Spring the tires all needed a little adjustment.
Up till this time I never had a light come on the panel before. The BAS ESP light came on a couple days after I checked the air pressure. I thought the brake switch went out since it is fairly common. I tried turning the steering wheel all the way one way then the other and the light would come off for a minute or so. So I bought a new brake switch and was going to put it on the next day. Then after reading the forum again I decided to buy a real good quality tire air gauge. The next day I checked the tires on my Tahoe and there were 3 tires low. So I checked the Crossfire and the right rear was 2 pounds low the left front was 1 1/2 pounds low and the right front was 1/2 pound low, the ,left rear was good. I thought great this may be the problem with the light coming on. I took great care to get all 4 tires just perfect then turned the wheels both directions again to reset the sensor. I took it for a drive and the light came on after about 8 miles. I checked the tire pressure again and it was perfect. Took off and the light was off but came on in about 6 more miles. Kept this up for 2 days of not being on when I start it then coming on with in about 8 miles. So I was going to change the brake switch the next day. Then the 3rd day it never came on again and it has been a week and a half now with no BAS ESP light coming on. It must have taken the sensors a couple days to read things right again.
All this because I trusted the air gauge built into my new Slime air pump.
This was the 1st problem since September 2003 when bought new.
I will post again if I have any more problems with the light.

 

I don't believe there is any reason a BAS ESP light would be involved with a low tire pressure
The air pressure triggers your TPMS light not the BAS ESP

Someone correct me if I'm wrong here

 

I did a forum search 10 pages back and searched the internet for the same problem in Mercedes cars. Found posts from several people that had the light go out after setting their tire pressure to the proper adjustment. So I tried it and it worked for my car so far.

 

That would be a first as far as I can remember. I have had my tires a few pounds up and down but no BAS/ESP light came on.
You did change your battery some time back and that may have triggered the odd situation, but not the air pressure.
I cannot quite see where the brake switch fits in the scenario either.
The pressure correction did not immediately correct the light On so I think you have made a leap in judgement on it. The light probably would have reset without the air pressure change. Coincidence I would say.