I have a 1997 3.2 TL and Im having some slipping/gear not engaging issues. Im 25 and she’s been around about 11years. Ive had possession and ownership of her a year and a half. Whenever I start her up, and go she drives fine. After about 20mins of riding, when i come to a complete stop then proceed to accelerate, she doesn’t move. My rpms go up(I push her nomore than 3000rpms) but she doesn’t move. I have to drop her into 1 before she moves(transitioning thru the gears up to 4 as I speed up). I’ve drained and filled her once within the last 2weeks of experiencing this. Also cleaned trans filter with carb cleaner.

 

I may have had similar issues last year with my 1996. felt like at times either it wasnt getting fuel, misfiring, etc. Push the gas and couldve been interpretted as the transmission not engaging.
Turned out to be the cam shaft sensor melting, a common problem in the 1st gen. My mechanic thought there was oil or something black along the engine block and it was the melted part of the sensor. Replaced and everything working great now. Maybe check into see if that area has black drips around it?

Good luck, not many of us rocking the 1st gen TLs anymore!