OK...I haven't played/looked at the ABS on my F150, but I had the same
problem as you with the ABS on my T-Bird, except that after the first
braking and pedal issue, the ABS light would come on detecting a malfunction
and deactivate the ABS system.  Now in the T-Bird ('93), the setup was a
small sensor aimed at basically gear teeth that spun on the hub.  The sensor
more or less sent info to the computer that determined the speed, and if
that wheel was turning based on more or less by how quick the sensors
signals were coming back through the gear teeth space as it turned.  The
computer took the info from all 4 sensors and how much pressure your
applying to the brake and made it's calculations.  What had apparently
happened was that debris or a rock got kicked up into the gear teeth and
bent the sensor when it came around so that it wasn't aimed at the gear
teeth anymore.  All I did was bend it back to where it was supposed to be,
by referring to the other sensor on the passenger side and it fixed the
problem for $0 and few minutes.   I'm sure the truck system is set up
different as I'm sure they've improved the ABS system since then (plus I
can't imagine that they'd expose the sensors like that of off road
vehicles), but I'd pretty much guess it's an issue with one of the sensors.

I'm sorry I can't help too much further other than see what info you can dig
up on the sensors....

IYM