What should one look at to diagnose a oil pressure problem that starts out on a cold engine around 35-40 but as the engine warms up goes to zero?

the cam bearings could be worn out. in which case you probly need to change. but when you pull apart the engine, you will probly find some other problems, so you might as well just rebuild the engine. its hard to beat those old Chevy 305 engines, they go forever and they make good power done up right

if the engine has low miles then it is likely an oil pump problem and the pump should be replaced...on a high milage engine then is likely time for rebuild....you could try using heavier weight oil or adding addatives like lucus oil stabilizer to get a few more miles out of it....

Like the first person said, it sounds like cam bearings. You can try thicker oil if you don't really care about the engine, it will let it go a little longer. I highly suggest NOT using Lucas or any other oil additives. They are no good.