'98 Wrangler, no reverse when cold

Please help me understand this. Five or seven years ago I I bought a high mileage Wrangler with a standard 3-speed automatic transmission. After two changes of filter and
transmission fluid and minor tigntening of the front band over these past years I assert that all is now well in the forward direction.
Reverse, however, remains a problem...but only when cold. No problem at all after a five minute drive. On a cold start I might be able to gun the engine and have it lurch into reverse. Also, if I let it idle in Neutral for a few minutes it might then be able to hard-shift into reverse with a mild clunk. Seemingly this warm-up behavior only occurs from Neutral, not from Park, but that's just a hunch.
I can live with this reverse situation, but I'm just curious about what the actual failure mode might be. Does anyone have any ideas? Any pointers to online "how it works" documentation?
--
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Jack Myers wrote:

Since I usually have at least one clunker around, I see this fairly often. Usually, it's a gummed up control valve and goes away with fresh fluid - some times just by topping off a low level. Major PITA but nothing fatal - unless you get on the gas really hard and slam it in.
Sometimes, just cycling through the gears (all of them) is all it takes, but it will get worse and worse until I change the fluid.
--
Will Honea


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On the old 3-speed Mopar Torq-Flite designs (aka AMC Torq-Command) the low-reverse band (inside oil pan toward the driver's side rear) would cause a no/harse-reverse condition if the band became too loose. Low /incorrect fluid can also.
The quickie test, if you have a tachometer in your instrument cluster, is to drive to a safe place with room to stop in and NO traffic of any kind and shift to 1st.
Then with the brake held firmly, accelerate the engine until 1/4 to 1/3 throttle is reached.
With the factory torque converter and tight bands you should not go over 1600-2400 rpm.
If the engine continues to increase rpm beyond 2400 then something is slipping in the low-reverse system.
--
Budd

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