Engine light is on an a dead spot when acceleration

there is no mention of a fault code reading ( very important as you will see)
you have covered everything and in doing so are overlooking logic
you have a dead spot on acceleration so by looking at possible areas of concern , there are 5 not mentioned
One is the accelerator position sensor
Quick acceleration may be causing a problem in that unit but the quick movement
next is the throttle control position sensor Problems there can be from faulty voltage from the APP , wiring or even a sticky throttle e action
Next is the ECM or a section of the ECM
The ECM controls the fuel/gas to the engine and you state that there is not a fuel/gas supply problem, the ECM gets its air /fuel ratio settings from the heated oxygen sensor in the exhaust manifolds before the cat converters, mass air flow sensors, volume air flow sensors, barometric sensor and ambient temp sensors
So logically if any of those sensors are not reporting in a timely period then the ECM becomes a bit confused and the dead spot will occur until it gets a second to recheck the parameters set in the CPU
Slow acceleration , is ok as the ECM is continually tuning to the throttle position but fast acceleration is throwing the system out
Lastly , in the Ignition control module there is an electronic advance / retard program that adjust the timing to exactly the correct rpm and throttle setting and if that unit has a fault , that is as if the timing is being retarded initially under the acceleration
another unit that has input into the ECM that reports on engine timing is the knock sensors that stop detonation ( pinging)under heavy acceleration by reporting the engine noise to the ECM which adjusts , timing and air / fuel ratio to prevent engine damage from the detonation

Year, make, model, engine size????? Probably a bad throttle switch id it is always in the same spot.

I guess I could buy into the timing belt idea. But, if it runs ok all other times, its not the timing belt. Especially if it idles ok and has power once it gets going. How many miles on it? Is the check engine light on?

The missing while accelerating is likely due to ignition coils and/or spark plugs going bad. The missing while in park is a normal thing. The car has a rev limiter that will not allow the engine to rev to higher than 3000 RPM while in park.

Is the check engine light on? Check the air filter check the TPS

Do you have the check engine light on at any time? If so, you need to get the codes scanned and make note of what the codes are.
It's possible the accelerator pedal sensor has a dead spot in it, causing the hesitation. It probably would be a good idea to have the throttle body cleaned (front side and back side).

Look under it for leaks

Fill hot--Mercon V


Check and test the TPS Sensor
on the throttle body (Dead Spot)

well it sounds like its time to change the timing belt.

Check your TPS Throttle positioning sensor. Sounds like it has a dead spot in it or it is failing. May also be a wiring harness issue or loose connection at TPS too! If its intermittent then it will soon go out completely. It should be located on your fuel pedal. Remove it and check it with an ohm meter. Check resistance all the way thru from 0-100 percent. When it is not working it should do nothing and show no resistance. When it is working the resistance value will increase and or decrease as you turn the sensor.

might be something simple as a wiring problem.. or the truck isnt producing the ryte amount a fuel pressure