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I,m sorry i,m the one to tell you the bad news But your transmission needs an overhaul,
See this is a common problem in a 1988 car, your Transmission The ZF4HP22
Is a well built transmission but unfortanally the Rubber O-Rings and seals Internally,from Age , Hot and Cold Tempatures get Hard and will not seal Properly until warmed up....
just like putting a rubber band in the freezer , It`s stiff till warmed then it will relax and stretch easily.
I would Not recommend any additive as it could do Harm to the internal parts that are still serviceable, a Minor overhaul will cost less than a full rebuild !
In the case we spoke of the trans being so well built you wouldnt want to wait months to have it repaired , see you may do more damage by waiting to long . Here on the East coast an Overhaul on the ZF4HP22 could run anywhere from $1000 to $1800.
Just Price shop first.