As mentioned, the kickdown solenoid is only suppose to kickdown into 2nd gear at wot. There are very few TH400 transmission calibrations that will do a 3-1 downshift about 20ish mph (the Buick Stage one, W-30 Olds 442, Ram Air GTO, some of the high performance Chevelle/Camaro/Impala) but those are very rare. I have been looking for that specific valve body for 20 years, with zero luck. I suppose it’s possible but very unlikely that someone swapped parts into your truck sometime in its history.
I would start by unplugging the kickdown connector at the transmission. That will eliminate the wiring and switch outside the transmission. Other than no wot kickdown, the transmission should function normally.
Still does it? Time to dig deeper.
Pull the govenor from the transmission. It’s located behind a stamped steel square cover on the passenger side of the transmission, near the rear of the trans. You will lose a very tiny amount of fluid. Make sure you have a replacement gasket, usually they tear taking the cover off. Inspect the governor gear and weights. Make sure the gear isn’t chewed up or loose on the shaft. Make sure the bore the govenor spins on in the case isn’t chewed up. The govenor should fit into the bore with no up/down wobble. If it moves around, the case is worn.
If it still does it, drop the transmission pan. Make sure the kickdown solenoid is tight. Depending on what style solenoid is used, it may or may not have a gasket. The oval can style used a small stamped steel gasket. The square open style solenoid has a molded seal on the bottom, and doesn’t use a gasket. If it was assemble incorrectly, it can cause a internal leak. Usually that causes a late upshift, or no 3rd gear. The solenoids aren’t expensive, it’s probably worth rolling the dice on replacing it. You will get the later style that uses no gasket when ordering a replacement.
If everything checks out, it’s time for valve body inspection. Or depending on how much crud is in the pan, transmission removal and autopsy might be needed.