When changes from 4th to 3rd (or 3rd to 4th) is very smoothly.
I perceive only watching RPM.

For example, if I run
constantly in 4th @ 44 MPH engine rotate ~1300 RPM
constantly in in 3rd @ 40 MPH, engine rotate ~1650 RPM

Are you able to monitor TCC lockup during all this?

I meant with your gear shift, not speed

I think I'm unable to do that report, cause even in manual shift from L2 to L3 position, it does not change to upper gear.

Well, I'm pretty new to automatic transmissions... I only compared speed/RPM at constant speed with that graph.


Right, I never tried this: I'll do tomorrow.

Just didn't want you to get confused with TCC unlocking/locking at that range.

If you're sitting in the car with the engine idling, can you not push the brake pedal and then select "1" ?

I tried this:
I changed selector from D at speed ~ 43 MPH/1300 RPM in position "3"
Then gear shift from 4th to 2nd
At this point I think my initial supposition was wrong,
now I think 3rd gear does not engage at all.


I think now this behaviouur is due to TCC locking/unlocking in 4th gear,
not gear shifting.


Understood,

Yesterday I tried this preliminary test:

At Stop, from "P" I selected "1"
run until 2500 RPM, then put lever to "2": gear changed to 2nd
run until 2500 RPM, then put lever to "3": gear did not change at any RPM
run until 3000 RPM, then put lever to "D": gear changed to 4th/overdrive

If it'* not shifting into third at all you likely need to put a good scan tool on it and see what is going on.
Is the shift is being commanded? What is happening with the shift solenoids?
I would throw a bottle of trans fix in it. You may get lucky.

You mean kerosene?

Okay, but here'* the thing: I gave you such a specific list of steps for a reason

1. Dead stop in "Park" <<<Now we know exactly what your configuration is as you are starting
2. Manually select "1" <<<Now we know you have selected 1st gear
3. Accelerate gradually until the engine is at 2,500RPM <<<Now we know you are doing 2,500RPM in the gear you are in, that might be the gear you selected or might not
4. Hold this speed for five seconds <<<Now we know you are stabilized at 2,500RPM in this gear
5. Manually select "2" <<<Now we know you have selected 2nd gear
6. What is the RPM now? <<<Now we know the difference that this gear change made, and can do a little math to figure out what gear it ended up in
7. Hold this speed for five seconds <<<Now we can tell if the torque converter clutch may have engaged or not, helping our math
8. What is the RPM now? <<<Now we can tell if the torque converter clutch may have engaged or not, helping our math
9. Accelerate gradually until the engine is at 2,500RPM <<<Now we know you are doing 2,500RPM in the gear you are in, that might be the gear you selected or might not
10. Hold this speed for five seconds <<<Now we know you are stabilized at 2,500RPM in this gear
11. Manually select "3" <<<Now we know you have selected 3rd gear
12. What is the RPM now? <<<Now we know the difference that this gear change made, and can do a little math to figure out what gear it ended up in
13. Hold this speed for five seconds <<<Now we can tell if the torque converter clutch may have engaged or not, helping our math
14. What is the RPM now? <<<Now we can tell if the torque converter clutch may have engaged or not, helping our math
15. Accelerate gradually until the engine is at 2,500RPM <<<Now we know you are doing 2,500RPM in the gear you are in, that might be the gear you selected or might not
16. Hold this speed for five seconds <<<Now we know you are stabilized at 2,500RPM in this gear
17. Manually select "4" <<<Now we know you have selected 4th gear
18. What is the RPM now? <<<Now we know the difference that this gear change made, and can do a little math to figure out what gear it ended up in
19. Hold this speed for five seconds <<<Now we can tell if the torque converter clutch may have engaged or not, helping our math
20. What is the RPM now? <<<Now we can tell if the torque converter clutch may have engaged or not, helping our math
21. Procedure complete <<<Now we can do some math to help figure out what'* going on

Maybe it really is shifting 1, 2, 4 . Maybe it is really shifting 1, 3, 4 . Maybe it is really shifting 1, 2, 3, then engaging the converter clutch. Maybe several other things. Doing this procedure will get us closer to helping you solve this issue.