What connections need to be cleaned? I have the same problem. The TSC off light comes on and it trips the engine light as well. I noticed that the cruise control doesn't work when the TSC off light is on.
TCS is essentially a function of the ABS module. You can pull codes with a Tech 2 or some other capable code reader (NOT a generic OBDII reader), which is what I'd recommend. Otherwise, you're going to be doing a lot of testing sensors and connections, etc. with a multimeter.