TRAC OFF warning light

This is a 99 GT 3800, 100K mi.

About two weeks ago The TRAC OFF lamp started coming on after restarting the car following about an hour of highway driving. (Drive on the highway for about an hour, stop for gas, etc., restart the car, TRAC OFF lamp comes on and stays on.) The TRAC button has no effect. If I turn the car off and then restart it, the lamp will go off. (The lamp will then react to the TRAC button as expected.)

The lamp never came on while driving around town or after short jogs on the highway until today, when it suddenly came on while driving at approx 35 mph on a smooth & dry city street after about 30 minutes of city driving. I pulled over, turned the car off, restarted it, and the lamp went out.

Any ideas?

Thanks in advance for your help.

loads of troubleshooting to perform but i'll try these first, check the wiring at switch and at the ebcm. look for loose wiring, poor connections, rubbed-through installation etc...
the ebcm turns the trac off indicator on when there is a low voltage, and when the circuit is not grounded at the ebcm the trac off light remains off.

the ebcm is on the upper left side of engine compartment, check the connector on the backside of what brake lines run into. the ground is the black/white wire, the traction control signal is brown/white, and the traction inditactor control is purple/white, traction active indicator control is light green.

yeah i agree s_jo4 that is a very good possibility the only other thing i can real think of right now is it might be something with the ecm the computer might think its on an it will stay on if the computer thinks that until its reset with a computer at a shop or if u have one - i got one it was only 2k an it helps out so many probs for me an other people.....

I have done what s_jo4 suggested in the engine compartment - could not find any loose or dirty connections, bare wires, etc. I do appreciate your clear description of the wiring. I am not ready to take the dash apart to go after the switch. For the sake of argument, let's say it's not the switch in the dash - where would we look next?

Thanks again for the help.