Mustang low oil pressure

Has anyone ever heard of this? I have a 66 coupe I completely rebuilt both engine (a 6 cyl 200) and tranny. Now they are back in and the tranny is fine but the engine has an oil problem. It started up fine after the rebuild but it starts with only 20 psi of oil pressure and after a few minutes drops to nearly 0. I have replaced the oil pump with a new one and then put the old one back which worked fine before. Both are doing the same thing. I have replaced the pressure switch and also hooked it up to a mechanical guage and still have the same problem. What could I look for next before I pull what little hair I have left out?

if it wasnt for the fact that you said the engine was just rebuilt i 'd say it sounds just like a bearing problem . how did the crank shaft look when it was out . did you check the bearing clearance with plastigauge

to me it sounds like once the engine is heating up the oil is losing viscosity and the pressure is dropping bc of the warm oil, dont know how to fix though, im no mechanic, but thats my theory only bc ive seen other mustangs do the same thing

Did you clearance the oil pick-up when you reassembled it?

i'd say maybe the oil pick-up tube is too close to the oil pan... i would try a shorter one...