It sounds like your inching linkage is sticking.

Check the linkage that the cable attatches to from the inching pedal to the top of the transmission control valve, disconnect the cable and see if linkage is binding or stuck,the linkage and inching spool valve should move freely with some slight resistance. Unbolt it from top of control valve, tear it down and clean it then lightly sand the shaft with emerycloth, apply anti-seize to the shaft and reassemble. Inspect the 2 O-rings and replace them if needed. We see this problem a lot in trucks that operate in high dust or dirt areas. If this doesn't solve the issue, start looking for a broken inching spring. Let us know what you find. Remember to change ATF and clean filter every 2000 hours for extended clutch pack life.

not on this forklift, since an operator must be in the correct position (sitting on the seat) for this unit to go in gear or lift/lower.
For you to be able to understand "if not, why?" you would have to understand how a transmission in this forklift works, but it is accurate to say the inching control works after the directional control in engaged electronically in the flow of power from the engine to the wheels.