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Do you know anyone else with an Explorer/Ranger/Bronco II with a 2.9 or 4.0? If you do, perhaps ask them to borrow their IAC for a second to try it in yours. It is not entirely impossible to get a new defective part, especially if it has been sitting on a shelf for a while.
This is really out there, but it could be the TFI module on the distributor. On 2.9s, this provides not only information for the spark, but Engine RPM and when to fire the injectors. I would say it is the possibility that its incorrectly reading the RPM and making the computer open the the IAC up, but since your Tach is working right, I don't really see that as that being it. If you have some WD-40, spray it around ALL the vacuum lines, everyone you see, and around the throttle body, IAC, and the manifold gaskets.
Rezvani's Latest Post-Apocalytic Monster Is a Ford F-150 Raptor Underneath
Slideshow: Called the Fortress, the 850-horsepower pickup combines Raptor underpinnings with military-inspired features, survival equipment, and a starting price of $285,000.