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There are two possibles that would cause the problem you are having.
1. A leak in the valve body.
2. A leak in the revers servo.
Please let me know how you would like to proceed with the repair of the trans. There is a 75% chance the trans does not have to come out to fix this problem. But please remember there IS a 25% chance that it will. I can walk you through the steps to do the repair if you think you can do the job yourself.
if there is a leak in the reverse servo how do you repair it
You will need to go to a local trans shop and get a lip seal for the revers servo and a filter "it will be much cheaper to get one from the trans shop rather than the auto parts tore" and then you will need to get some rtv black to reseal the pan and 5 quarts of fluid to refill the trans with. These are all the things you will need to get to repair the revers servo. You will need to pull the pan from the bottom of the trans, pull the shifter lever off of the shifter shaft, drop the valve body " pull all the hex bolts and leave all the torques bit bolts alone and the valve body will come out as 1 piece". From there you will need to take the band adjuster bolt out and then you will need a pair of snap ring pliers to remove the servo. Pull the servo and replace the lip seal on the end of the servo then put everything back together. Let me know when you pull the servo and i will have you tell me what you see and if there are any "chunks" missing. Here are some diagrams of the servo location.
Here are the links to the diagrams you need.