I don't have access to a 825I workshop manual, but I'll describe what's done on the 885D as it is likely similar in nature with respect to the bed lift.
The up/down switch sends low current power to two relays which have a high current lead. Therefore two fuses are involved, one to raise it and the other lowers it. The low current source the switch provides to the relay is a switched circuit meaning it is on when the key is on. Wire color is likely yellow. It might be F8 (15 amps) located on the ECU. Under the storage tray.
The power source for the electric pump (red wire) is a 40 amp fuse in the fuse box (mine is high on the firewall behind the brake pedal) and is position F. There are only four fuses in this holder and no other components. (People have reported corrosion issues with this fuse block, so you may want to take it off and investigate its condition.
If you're bed isn't raising or lowering, I'd check for battery voltage at the bed lift switch when key is in run and check for battery voltage at the two relays with key either off or run. Doing this simple test will isolate the circuit making root cause easier to find.
Remember! This is based on the 855D manual.
Good luck and report back what you find.
2012 JD855D OPS Black Poly Roof, Deluxe Cargo Box, Front and Rear Protection, Power Lift, Front Hood Rack, Rear Screen (homemade), 800 Watt Inverter, 2500lb Winch installed in cargo bed, Front and Rear LED auxiliary lighting (4" square 27 watt), Front and Rear CV Guards, Koplin Side Mirrors