I have a 95 Buick Century that gets a bad vibration when the TCC engages. This vibration goes away if the car downshifts to accelerate or coasts. I already replaced the CV axles as it was suggested originally that they may have been responsible but now it's looking like the TCC is bad. I'm looking for the electrical connector that goes to it to see if the problem goes away with the TCC disabled.
The connector is usually just above the pan on the transmission. A 95 likely has an E series transmission which means that the same connector will also have the other transmission controls in it. If you remove that connector the transmission will stick in 2nd gear and your engine wont run correctly because the computer thinks the transmission died.