Yup, the primary function of the TPS is to govern the 3-4, 4-3 shift.
If the TPS is dirty, worn or pooched it will mess up that shift.
First thing to do is check the voltage on the TPS with the ignition key 'ON' (don't start the truck). With the key on, you need to use the center wire for your "+" probe on the volt meter and the negative can be connected to the battery "-" terminal.
Make a note of voltage. Normally it will range between . 6vdc and 1. 2vdc.
Second, with the voltmeter connected, cycle the throttle slowly and smoothly to WOT. Watch the needle... is should move upward in a smooth non-twitchy movement.
The upper end voltage reading when the throttle is at WOT should range between 2. 25 and 2. 75 volts OVER the at rest voltage.
Raising the initial voltage will delay the 3-4 shift, and lower it will make the 3-4 happen sooner.
He should also make sure that ALL his connections under the hood and on the trans. are clean and free of dirt or contaminants. The TPS is not the only sensor/controller that is tied in to the PCM, all of which has an effect on transmission, engine, and pump functions.
Hope that helps... .
Pastor Bob.