Throttle linkage determine upshift point for WOT.
Vacuum modulator does for the rest of the throttle positions.
If you find both in good shape and adjusted correctly, you may have to remove valve body and give it a good cleaning and emery cloth the valves. Clean with Brakleen and assemble with ATF. Make sure weights in governor are intact , these are located on the output shaft, jack car up in the rear, use stands, rotate driveshaft slowly, you can hear the weights move on their axis inside.
Do a line pressure check at your local trans shop, to make sure oil pump is up to snuff. Second gear is a locked up planetary gearset via a piston driven by oil presssure from the oil pump. If not enough oil pressure, no 2nd gear.
Food for thought