Both the flywheel and cam position sensors on the 3.8 are Hall Effect which means they can detect a static object, They are not Variable Reluctance sensors which do have minimum speed requirement but the automotive world has pretty much moved on to Hall... and for many years now..
Of course what the ECU does with this position information is a whole different ball game, it may be being discarded as "not credible" due to the low crank speed.
The 3.8 will "run" without a flywheel sensor ( but not well, and its certainly not happy ) but it may require a few tries to get it to start.
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It seemed like a good idea at the time........
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