I had the same problem with my 1986 Ford 250 with the 460.
The 460 has an oil pressure switch inline with the
power line of the fuel pumps. When you turn the key to
START there is a bypass circuit that kicks on the fuel
pumps and they charge the fuel lines, regardless of
what the oil pressure switch says. However once the
key is released to the RUN position the bypass circuit
is turned off and the primary circuit takes over. This
is why it runs for a bit then dies.

It seemed like my pressure switch was stuck or
something else was goofed with it. I say this because
the truck was doing this and I had another problem so
I had it towed to my mechanic. Once there there truck
worked fine. A few months later the problem crept back
up. I found the switch and bypassed it and the truck
ran fine. I then changed my oil and oil filter and it
fixed the problem. The oil was pretty old as its a
farm truck.

The switch is located in back of the engine on top.
It's a freaky looking thing that looked like it could
also have vaccum hoses attached to it if I recall.