No reverse while cold

Hy every one,

i've got a funny problem on my truck.

Firstable, the truck. a 96' Tacoma with 3RZ engine and auto trans ( A340) 4X4.
About 180 000 miles on it.

I buy the truck 6 month ago and have to replace the head gasket cause the previous owner run the car for month without water pump (This engine is bullet proof...)

Since i've got it i always have a problem with reverse. The truck never go in reverse when cold. I have to drive for more than 20 minutes to get the reverse working. Even when the engine ( and the oil is hot) sometimes the reverse won't engage...

When i've got the problem i notice then when i put in reverse and accelerate, the truck begin to move backward a little bit. just few centimeter for 1 to 2 seconde and then it hold like i was in neutral.

I try to replace all the oil in the auto transmission whith new one ( I use some dexron 3, it mention to use dexron 2 but it's no longer available).
We don't have valvoline or U.S kind of oil here in Tahiti. Just Mobil - Shell - Total - Motul
I replace ALL the oil ( about 9 liter) even in the converter.
No change,

I remove the pan and clean the filter, it was a bit dirty ( normal with the car running without waterpump for month...) but nothing to mention.

Do you think it can be a solenoid problem?
or maybe the oil i put in is not the good one?

Please help, i have to calculate all my moving without reverse....

Thanks!!

 

Sorry i don t understand.
What is it supposed to be?
Thanks!

 

@gearcruncher is the forums trans guy. The last PM I had with him he is inundated at his shop. You could try sending him a PM and see if he replies.