I have a '93 4.0 which has had the oil cooler removed, and a by pass put on. After a drive of an hour or so oil pressure is way down at idle. Is this OK or should I replace the original cooling system?

 

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The oil cooler by-pass was a factory thing.

Not many markets got the cooler on the 6 cylinder.

My X300 3.2, and the X300R (Supercharged), do NOT have it in our market, and we are a tad hotter than the UK. Different body, I know, but same engine.

If you are losing oil pressure, or appear to be, I strongly suggest the fitment of a mechanical Master Oil Gauge, and verify the truth. The electrical sender units are well known to do odd things, as are the instrument units of the dash cluster.

Oil viscosity has a small affect on pressure, but not much.

This is Parts drawing of the oil filter housing, showing the factory by-pass elbow as #4.

 

Someone please correct me if I'm wrong, but I think the oil pressure sending unit on a '93 4.0L is the #JLM20791 type, which is really just a binary switch. It is either 'on' or 'off' so it couldn't indicate any reduction in oil pressure other than zero.

You may have another issue, like a heat related wiring fault that is interfering with the signal to the gauge.