Hi,
I agree, the very first thing to check is the oil level and top up as needed.
Keep in mind that the oil serves two purposes in an OD gearbox: It provides lubrication just like a non-OD gearbox, of course, but also hydraulic action within the OD itself.
When the OD is first used after a rebuild, i.e. it's "dry", it will fill up various parts of the hydraulic system and should require topping up right away. Later, when you change the oil with the gearbox/OD in the car, it never all completely drains out. So a fill from "dry" takes more oil than a refill after draining.
Also important is the *type* of oil being used. I'm sure you got advice about that already, from your rebuilder. Just be very certain to use a *non-detergent* oil, such as a racing motor oil. Foaming action in typical detergent motor oils will cause air bubbles to get within the OD hydraulics, which could cause the OD to stop functioning.
Personally, I'd not use a synthetic motor oil in there either, even if a non-detergent type could be found (many or most synth motor oils are high detergent/high mileage).
There are some specific non-detergent synthetic gear oils available, some even with friction modifiers. But I'd even think twice about using those in any TR gearbox. Problems (mostly popping out of gear) have been directly traced to using synthetic oils in TR g'boxes.
The next most likely suspects are the solenoid, wiring harness connections and switches, or some adjustment of the OD actuating mechanism. After that, the innards of the OD are the next thing to consider. But, I'm not all that familiar with the J-type in these respects, so can't really make any suggestions.
Another thing that can be tested, after all the above have been eliminated, is the amount of hydraulic pressure being generated within the OD unit. Again, it's different (much lower psi) on the J-type than the A-type I'm familiar with, but with the right tools it's pretty easy to check.
Hope this helps!