What does this light mean, and should I be concerned with it?

 

ASR is a type of traction control.So most likely if it comes on is because you have wheel spin.

 

The light stays on. Could this indicate a problem with my TCS?

 

its a possibility

 

Did you just buy the car, and/or has the light always been on? From the factory, the traction control is active unless you switch it off. You can buy a module that reverses that action and leaves T.C. off (light on in the dash) until you switch it on to activate. Have you played with the switch on the center console dash at all to see if it does anything?

 

I did just buy the car from a lady about 2 weeks ago. And as far as I can tell, the light has always been on.

It is a '94 z28 6 speed, and I have no idea what switch you're talking about? Maybe its an automatic thing?