Ya, look at it this way, the pedal controls the throttle linkage and nothing more. On an fi car, the idle is purely controlled by the idle air control valve, which is run purely off of the ecm sending volts to it, it has nothing at all to do with the throttle linkage and is not at all connected to it. It will correct to an extent any extra air that is coming in from other sources like a vacuum leak.
I honostly have no clue why your pedal would do that when you start it, makes 0 sense. The pedal sinking at high idle just is not something that should or reasonably could happen. Im not saying it does or doesnt do it but it just doesnt make any sense to me outside of maybe a really weak throttle return spring and a really strong idle vacuum causing vacuum to pull your throttle blades a little bit. But if that was the case, youd have throttle sticking open issues galore.
Check your linkages, clean your iac, check your tps, replace your ball and check for vacuum leaks.
Did you get a prom burned for the 406, put in higher flow injectors or do anything else with the new motor? A little more background would be helpful

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