OK, well fast cycle indicates it is not building any hydraulic pressure so stuck check valve or bad seal on the hydraulic piston, or having low oil has sucked a bunch of air and it has not purged it from the system(air in the system = no work = fast tunk tunk tunk). Not blowing oil out the air exhaust is a good sign
No oil in the main reservoir will eventually cause you problems with the hand pump as the hand pump reservoir is just a little smaller than the cab lift required volume, and it makes up this difference by sucking fluid from the AOP reservoir. eventually you will start to send air to the cab cylinder near the top of the lift and each time you lower this air comes back last sending more fluid to the main cracked tank to leak away. eventually you will start pumping air early enough in the lift that you will not be able to complete the lift.
1. You first need a reservoir that is not leaking. You can try and buy one, or have a local weld shop fabricate you one(I would fab a steel one). In the meantime, I would probably try and pull it and seal it(degrease and duct tape, or epoxy) for testing.
2. once you have a reservoir that holds oil, fill it, disconnect the supply and return lines and and connect the ports together and run the pump to purge air from the AOP, then reconnect the supply and return lines to their normal ports.
3. Next select cab raise and disconnect the cylinder base line at the cylinder and run it into a container and again cycle the AOP to purge air from the line and valve and reconnect the line to the cylinder.
3. Remove the filler plug on the hand pump(rear outboard corner allen head plug) and completely top off the hand pump and reseal the plug...
Now you can see if the AOP works. Try and lift the cab with the AOP. should only have a few rapid "tunks" until it builds pressure and drops to a more slower/labored clunk as it performs work and lifts the cab...