At higher mileages, (125,000-150,000) the automatic transmission may not shift correctly. This can be caused by the throttle position sensor being out of adjustment or a shift solenoid needing to be replaced. Typically the transmission does not need to be completely overhauled.
Automatic Transmission May Not Shift Correctly at High Mileages on Toyota Cressida
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1991 Toyota Cressida began to not go from 2nd to 3rd gear until very warmed up and would work only after shifting through all the gears and reversing back and forth before getting into traffic. Problem eventually worsened and it now will jump gears while driving and/or will not go into gear after stopping in traffic. I have to shut off engine and restart to "nudge" it into gear at a stop light, or if moving, must put into neutral and turn off and then on while driving down the road! Very unsafe at this point; my very excellent mechanic says it is probably the shift sensor solenoid(s) - may as well replace both at the same time. Am purchasing a kit and he will install. Some worry as to after-market parts...mechanic does not recommend any made in China, for instance. Good news is we already drained and filled the transmission and really do not think anything is wrong there. I just hope the solenoids being replaced is going to fix it--it is still a fantastic engine!
It's a 1989 Cressida
Sounds just like this could be the problem. Car shifts out of 1st gear at over 2000 RPMs when cold and seems to be okay when warmed up.