Technical Oil loss, where?

I'm leaning toward the fuel pump. If only for the reason that all cylinders are fairly equal in compression, deposits and such. I am not familiar with Packards at all, but could the oil get into the fuel through the pump?

 

Yep, if the diaphragm is punctured.

 

Maybe the vacuum diaphragm in the pump is bad, not the fuel side. This would allow oil to be ****ed into the intake tract where it would be evenly burned in all cylinders, so you maybe wouldn't show 'excess' oil in any one place or enough to show at all. I'd try byp***ing the vacuum side of the pump and see if the problem goes away. If the car isn't running, pull a vacuum on that side of the pump and see if it holds; if it leaks down, I'd say that's the problem.

 

You gents above are thinking what I am, although I can only recall fuel getting into the oil instead. A vw I had many years ago was actually "gaining" oil. An older mechanic grabbed the dipstick and set it on fire with a lighter to confirm his diagnosis.