The vehicle has a cable that runs from the throttle linkage to the transmission. You can find this cable under the hood. It arrives from the passenger side and connects to the linkage via a ball and socket joint. There is a rubber boot right before the joint. Disconnect the ball and socket joint so the cable is detached from the linkage. Pull the cable out and slide it back and see if it moves freely within the sheath.

If the cable is binding and won't retract with the linkage, the transmission will shift late in all gears.