Did some digging around on the oil cooler thing...
The thingy that the water hose goes into in the middle of this picture is called the waterhouse (
according to SOR).
The waterhouse top comes in two versions:
054-16B TOP WATERHOUSE-1968-1/79 NO OIL COOLER
054-16C TOP WATERHOUSE-8/76-1/79 W/OIL COOLER
So clearly Toyota made some rigs with an oil cooler and some without. I am guessing it was an option.
FWIW,
This diagram shows the components that make up the oil cooler.
And this page shows that there are two different oil filter assemblies (one for oil cooler equipped rigs and one for not).