The oil pressure at higher rpm while driving is what matters.
The manual for the late 235 calls for 35 lbs. of pressure at 2000 rpm.
On a used motor you could have a little less and you may see almost zero oil pressure at idle after it's fully warmed up and especially after driving on the freeway for a while.
No need for rebuilt if it doesn't burn oil and you have good and even compression on all cylinders.
It can go for a decade or more that way daily ... speaking from personal experience.
Oil pumps hardly ever need replacement or repairs. If its all clean without build up down there I wouldn't be worried about the pump.
There is a relieve valve piston and spring that could be stuck in the open position, but that is also pretty rare with a clean engine.
If you remove the valve cover when hot and the rockers get enough oil and the pushrods are spinning, you are good.
Do you have hydraulic lifters or solids?
Valve lash should be adjusted when the engine is fully warmed up.
