If the trim is not externally leaking and is full then one or more of the valves are hung open. The hydraulics of the trim are one area I never recommend the owner mess with. Take the wrong part out and the hydraulic fluid can come out with tremendous pressure or small check valves can come out and you not even knowing it.
That being said, what you can do is to drain and refill the unit. I won't guarantee this will work but lets try this.
Tilt the engine all the way up and put on trailering legs.
Look into the cavity where the manual relief valve is, there is a single C clip. Remove the C clip. Holding a rag over the Manual relief valve and slowly remove the valve. When out put a large container under the unit to catch the spilled fluid. Examine the valve for any cuts or tears in the O rings. A kit is available from Evinrude for the trim that includes O rings.
If the O rings are not perfect, replace them.
Put the valve back in once the unit finishes draining. Check the old fluid for any signs of metal or contaminants.
Tighten the valve and refill the unit. Now try to operate the unit up and down a few times allowing the trim motor to cool between every few cycles. Keep the unit filled with fluid. If it doesn't come down when trimming down from air in the system, open the manual relief valve 2 turns to allow it to come down. Close it and try again. You may have to do this a few times to bleed all the air out of the system.
Once the air is out of the system see if the trim works and holds. If not then contact the seller. In more than half the cases this will cure the problem with new fluid and allow the bad check valve to operate properly. When used units are sold they are almost never overhauled unless there is a problem and if the guy isn't qualified then overhauling is about worthless. I certainly couldn't overhaul a unit and sell it for a profit at $420.
Try this and let me know how it does.