When the Tranny light come on You will see CHECK TRANSMISSION
along with chime.
Traction control light will just display TRACTION CONTROL or
CHECK TRACTION CONTROL if there were a malfuction with the Anti-Lock brake sensors on the brake calipers.
All these cars from 95 to 2002 have the Check Transmission Indicator in the message board. For it to come on and off frequently, I believe it's not possible. I've seen these messages come ( on these cars ) on after almost 45 minutes of use and when they do come on, they stay on until you shut the car down. Or if you are low on tranny fluid, it comes on almost immediatly after startup. But it doesn't blink on and off repeatedly after it goes off.
If it is the transmission, do a Tranny Fluid/ Flush/and filter change. When you want to chack the tranny fluid level, you have to have the car running to accuratly see the true level. And it you want to see if your fluid is still good, the fluid should be an almost clear light red color ( Mercon V or Mercon 5 ) both are the same and thats the fluid you use if you change it.
The Traction control light will come on everytime the wheels slip, thats if you have the traction control activated.
I find it odd that your mechanic is charging $1000 to just check the trasmission. A tranny job on these cars usually ranges from $1200 to $2000 if your mechanic is honest & that includes repairing your problom. It's not the transmission that costs a lot of money, it's the tight space to work because of that Huge V8 engine in the way. $1000 to just check it out is too much, so how much would he charge fixing it of replacing it???
Most common tranny issue with these cars are the Torque Converters from the 1999 to 2002 years. 1995 - 1998 has an advantage becuase it has 15HP less so they don't force that little FWD Tranny that much. If you have a bad Torque converter, usually you would know if you hear a whinning/scrapping noise at a cold start.
Live up hear in Snowy Connecticut so I now what these cars do in the winter. Plus I've been drinving many of them since 2003.
How many miles u'r car has?