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I found that if I park my truck facing downhill, the oil pressure comes up almost instantly.
If parked facing uphill, it takes a couple of seconds to get there. My guess is that this is because the oil pump is mounted on the front of the block and is submerged in oil when I park facing downhill. Parked facing uphill, the pump and tube probably drains and has to refill from the deep part of the pan before it can pump up into the engine.