@AE5TE
The Discovery II basically has an old 60's Buick engine, and you are right for the most part the low pressure light comes on at 6 psi.
AMC owned the engine for a bit and also used the timing cover design concept for the 304-360-401 (and 390 series) engines and Buick did the same for the 350-455 engines.
As the V8 engines age- oil pump end play (steel gears on aluminum housing) and excessive front cam bearing clearance is usually to blame for low idle oil pressure. It is common to see "0" psi oil pressure at hot idle on these engines. Not necessarily a problem, as the crank and rod bearings have much tighter clearances than say a Chevy small block, and tolerate it. But regardless, there are a few approaches from the Buick and AMC crowds to deal with low oil pressure at idle on this timing cover design. The V6 is hardier and has less of a problem with oil distribution front to back, but certain mods to raise the oil pressure apply to both the V6 and V8.
First is to make sure oil pump gear to housing clearance is not excessive. There are several kits for correcting this (or there was when I dealt with my Buick and later AMC engines). Also for my Buick I found a high volume kit which I believe has already been mentioned. This can be done in the driveway without too much trouble.
Second, check the output port from the pump cavity. On the AMC timing covers, it is greatly undersized. Opening up the port drastically improves oil pressure at idle. I do not know if this comes into play on the early V6. But if you are in checking end play, you will be able to see the output port. Modifying the port is difficult unless you have a 90 degree dental drill, but if you can figure out a tool then it is doable with the cover on the engine (at least in a Wagoneer).
Lastly, the engine has non priority oiling. So if there is oil loss anywhere the whole system drops in pressure. Years ago I did find an AMC based performance company that offered push rods with smaller orifices. This helped prioritize oil to the cam and lower end, with reduced flow to the rockers (which is excessive anyhow). This helped bump idle oil pressure a bit.
I would not worry about a click, persistent or not, in the valvetrain. Wear can be on the cam, lifter, pushrod, rocker arm, or valve stem. Where do you start in a non adjustable rocker system???? As long as it just a "click" and not a "CLACK" sound it is just normal wear over time. There is always the option to mill the rocker arm mounting bosses and install small block Chevy screw in studs and Chevy adjustable rocker arms. On a full rebuild it may be worth doing from the start, but I wouldn't bother going back in to do it!
It has taken me many years to no longer worry when I see low oil pressure at hot idle on this oil system configuration. And take everything I just wrote with a grain of salt, your engine version may have an updated system and I have never seen the Land Rover version of the engine. But if the oil pump and filter hangs off the right side of the cover, all I wrote should apply.