Looks like the problem you have originates from the steering gear, not the pump. This assuming that you had everything for the LHD conversion, cooler pipe and hoses included, (p/n 44420-60230 - for progressive steering) and installed everything correctly. You should check that the pressure hose, return pipe / hose and reservoir to pump hose are flowing freely, and since the pump is new, the only remaining suspect is the steering gear.
The valves for progressive steering are slowly closing the faster you go, and thus allow less fluid to go trough the steering gear. If you disconnect the wiring, in theory the valves should remain open. But it's also possible that without wiring, the system is just bypassing the steering gear, and the fluid coming from the pump is just flowing back to the reservoir.
But anyway, as the LHD steering gear was not new and you don't know for how long and how it was stored, I'd recommend a complete overhaul. If it's not holding pressure, the fluid is just flowing freely trough the steering gear and back to the reservoir.
If you want to skip the progressive steering, the best would be to look for a standard steering gear, I wrote the p/n in my previous post.
