what else might cause this problem?
Not enuf info, Charlie.
The Nash is switched by the ECM (grounds a pin on the relay) if certain conditions are met. The relay electrically activates the clutches in the O/D. The logic changed through the C-4 years, and as noted above, many owners tired of the complicated factory logic and opted for control exclusively through the switch.
The factory logic requires the car to be in closed loop conditions, which is somewhat related to temperature. In open loop, the car is not looking for any sensor feedback as things are not warmed up and giving good information to the ECM. Hence, the ECM has certain parameters to control the engine which are limited.
When the ECM senses closed loop conditions exist , part of which includes coolant temperature, it begins to take oxygen sensor voltage information and such. The system now relies upon its sensors; a closed system.
I have seen old oxygen sensors and bad plug wires foul up the overdrive. I posted elsewhere that I fixed a cycling O/D by changing the plug wires--ONLY. I reason that my O-2 sensor was reading a very rich condition, due to less-than-complete combustion and a rich mixture, due to the low vacuum caused by a hotter camshaft.
You see, when the ECM senses lower vacuum, it thinks we have 'our foot in it', asking to accelerate. Therefore, it dumps more fuel into the intake system than is actually required. The ECM can correct and learn, to a degree, but has maximum corection limits. Once it has taken all the fuel out that it has authority to take, that's it, unless your chip has the fuel tables remapped to reflect your engine.
The chippers adjust the tables by accessing the corrections the ECM is applying to try to attain a prefect fuel mixture, for all operating conditions. It is a large task. When you unplug your ECM's power for more than 10 secinds, you are erasing all of this learned information. Sometimes, that is good.
Sorry about the length.

Mike
What was the question?
Oh. If closed loop exists, your foot has not tripped the kickdown, and certain speed parameters are met (differing logic), the overdrive is available, via the switch.