Welcome to the site!I have an 02 Gt with the t/c.All i do is push the button and the light comes on.Maybe check and see if the connections are good/or the button is good.
I believe your wheelhop is from the irs, not the tcs.Yeah I have the same problem with my 99 cobra. The light is off and I still can't spin my tires. I mean they will spin but then hop. When I turn the light on it does the same. It sucks because I can't do a burnout.
Is the ABS light on the dash on? If not, does it definitely work? If there is a problem with the ABS system the TCS shuts off automatically! Let me know, if this is the case i have something else for u to check.well my light is always on, even when i press the button nothing happens, it stays lit. which leads me to believe that the switch doesnt work so my car is stuck with TC on i believe.